Doson
Thanks for the congratulations!
I haven't much experience in Rotations, but I have been thinking about a good team for this mode just a few days ago, and coincidentally, bulky booster Blaziken has also been part of my thoughts, though I didn't plan to use Baton Pass and had considered Bulk Up as an alternative to Swords Dance (but Swords Dance probably fits your team better). Unfortunately, I didn't try it yet (in fact, I haven't even bred it), so i can only provide thoughts based on theorymon, not on actual playing experience.
I think Protect + Substitute + Leftovers is the better choice compared to Protect + Focus Sash; the latter is quite vulnerable to random additional effects like paralysis, and you can't even make much use of your free attacking slot because Flare Blitz and Focus Sash don't go well with each other and Blaziken's other reliable STAB moves are Fire Punch and Brick Break (Low Kick is also an option, but unreliable in terms of damage output, and Superpower probably isn't a good idea on BP Blaziken in general), which are both pretty weak, especially with no investment and no boosting item.
Protect + Substitute, on the other hand, allows you to get more than enough speed boosts quite easily, as long as you don't rotate it into a faster opponent (rarely a matter as you can get a safe speed boost just by protecting) or an Infiltrator/sound move user that poses a threat to Blaziken. To work consistently, however, I'd invest at least 76 Speed EVs with a Jolly Nature, which allow you to outspeed Base 111 pokemon after a single speed boost, and also makes you faster than bulky Volcarona with an equal number of speed boosts, which is quite useful considering Volcarona is one of the most annoying and dangerous pokemon in Rotations (even if you choose to use not attacking move, it still allows you to possibly evade a Hurricane by putting up a substitute). Though you might as well consider 92 EVs for Base 115ers like Starmie and Raikou or even 172 EVs for Base 130ers.
In addition to that, I would either maximize the HP, or use 188 EVs, which hits 179 HP, thus giving you the highest possible HP number that makes four turns of Leftovers heal exactly as much health as one Substitute costs, which allows you to put up seven Substitutes with Leftovers and Protect (if I didn't miscalculate, this is also the highest possible HP number for Blaziken that can accomplish this).
Then I would put the rest of the EVs completely into one defense stat, because Blaziken won't reach much mixed Bulk anyway and if you focus on one stat, your Sub may survive some resisted (or very weak) attacks from that side at least.
Then, you'd have Sub/Protect/Swords Dance/BP, but to be honest, I'm not really convinced of the effectiveness of the BP setup. Setting up Attack boosts with Blaziken certainly isn't easier than setting up Attack + Speed boosts with stuff like Dragonite. Sweeping with +2 or even +0 Garchomp (if the opponent lets you get to +6, he was probably so harmless that Dragonite or any other strong booster would have swept as well) also isn't significantly easier than with Dragonite. What advantage does this setup have then? I see it more than an additional risk (the opponent might hit Garchomp with a strong attack or a side effect if you cannot pass a Sub, the setup cannot be executed if just one of your pokemon faints, etc.), and the Battle Maison is all about minimizing risks.
If you want to support your team members to sweep, you have other options like Double Screens (you already thought with your Metagross, so maybe this idea can be developed further), Aromatherapy/Heal Bell, Leech Seed and Wish. Those can all be utilized by defensive pokemon, so they a) other than no attacks Blaziken, can do something on their own by stalling out quite a lot of pokemon, b) are more likely to successfully execute their supporting role against most opponents (assuming Blaziken has to pass at least one attack boost to 'successfully execute its supporting role') and c) even if they happen to die due to a mistake or unavoidable risk, setup sweepers like DD Dragonite are still very strong on their own, while Garchomp is quite reliant on the support from Blaziken (although it's not bad on its own, but stuff like DD Dragonite is just much more self reliant).
Summing it up, I think Blaziken on its own isn't as useful as a supporter like Vaporeon, Mega Venusaur (with Leech Seed) or similar Pokemon, while I also think Garchomp on its own isn't as reliable and strong as other sweepers that are usually supported by the likes of Vaporeon. Also, if the strategy is successfully executed, it doesn't really give you a higher win chance than if you successfully execute a 'support your Dragonite with Wish' strategy. So all in all, I think Baton Passing is an inferior option of supporting team members in Rotations and probably would rather try a different strategy (maybe you could keep Blaziken and use it as an attacker instead of Baton Passer; mono fire might be viable, most Flash Fire users should be setup fodder for Dragonite anyway).
However, this is just theorymon and if it's really effective or not so can only be found out by actually playing in the Maison, so I definitely don't want to discourage you from giving it a try.
Regardless of what you decide to do with the Baton Pass strategy, I'd like to share thoughts on the rest of your team as well:
I think Metagross in Gen 6 is somewhat underwhelming; it has solid defenses, but not recovery and too many weaknesses to stall opponents out, it has good attacking power, but neither boostmoves (well it does have Hone Claws, but Swords Dance is a far more effective boostmove in general) nor an almost unresisted and thus easily spammable strong attack, and it can use Screens, but it's rather slow and will often have to take a hit before setting up the screen, so it's not really ideal in any role, and i don't think something that can do much but nothing really well is really good. If you want to go the screens route, Klefki has a superior typing and Prankster, if you want an attacker, Aegislash and Scizor would probably be more effective, and if you want a defensive pokemon, pretty much anything with decent bulk an reliable recovery will probably do that better.
Dragonite, on the other hand, is a really great pokemon for Rotations and for the Maison in general. I don't think it really needs Extremespeed though; as Trick Room teams generally consist of lots of bulky Ghosts and Psychics, the move probably won't help you at all against this matchup.
Also, after one boost, Dragonite already outspeeds most important opponents, and after two boosts it's faster than any relevant opponent in the maison. If you want to be able to hit Base 130ers after one boost, I'd rather try Jolly than use Extremespeed, which won't OHKO anything anyway (even Jolteon survives). In my opinion, Roost is the far better option. Another option is Substitute, which I really like on Dragonite in Rotations; however, I did always use it with Wish support - without it, it would probably either have to drop Earthquake and thus be walled by fairies (and to some extent steel types as well) or drop Roost, which doesn't allow you to set up much Substitutes so I don't think that's a good option.
If you decide to use it with either Roost or Wish support, you may also consider a more bulky split. I used 196 HP / 92 Atk / 4 Def / 44 SDef / 172 Spd with a Jolly nature, which allows it to outspeed neutral Base 80s without and positive Base 130s after a boost; also, it gets 191 HP, which minimizes indirect damage from weather, Leech Seed, Poison, Burn etc., though with Substitute, you can avoid most of those anyway. In addition, this split also always surives Modest Articuno's Blizzard (if it doesn't crit, so 95,625% of the time to be more exact), the rest of the EVs is put into attack. At first, I was sceptical that it would lack damage output, but it didn't matter in almost all battles because Dragonite still did a lot of damage (I used Outrage, Dragon Claw might indeed be somewhat weak) and very often, it could just set up two or three or four boosts easily if needed. That only applies to sets with recovery, if you don't use any, going fully offensive is probably the better choice.
Well, I already talked about Garchomp in the part about Baton Pass, so i can't add really much here, though if you want to try Baton Pass, you might think about giving your receiver a Lum Berry (Dragonite does like having the Lum very much though, but Leftovers and possibly Weakness Policy [though i don't think this would be an ideal item choice in rotations, since you will often have to take random neutral/resisted moves breaking your Multiscale followed by super effective moves that kill you before activating WP; roost could possibly reduce this problem though]) to minimize the risk of random additional effects and partly status moves. Non-Mega Garchomp and Haxorus (who bypasses annoying Sturdy abilities, as well as Levitate and others) would work similar and can hold a Lum Berry, though Haxorus' special bulk is somewhat lacking so it's not without its weaknesses either. Another option would be Mega Charizard X, who is immune to burns and can remove freezes with Flare Blitz; paralysis really hurts it though, and when switchin in, it still has the glaring Rock weakness from its normal forme (and in general, it has a lot of shared weaknesses with Blaziken + Dragonite).
