What exactly are you running on your Hawlucha then? Just wondering since you don't seem to be running into the same problems as others in this thread when it comes to it. Obviously everyone's mileage is going to vary depending on which simulator they play on or if they're just playing off the cart. The main difference being that the cart doesn't have access to Flying Gem to make the best of Unburden and Acrobatics.
Also wouldn't Hawlucha lose its stat boosts once it baton passes (if you're running it) or gets phazed out? What happens then? You have to start over from scratch. Except this time nothing to trigger Unburden. Nevermind counters.
But then again Hawlucha should have a team to back it up...
I haven't run a Flying Gem since it became obvious that it wasn't going to be available in-game, and I play on both the cart and on Showdown. I've had success with the same set on both formats. I haven't really settled on an item, but have been switching between using a Red Card and a Lum Berry with Acrobatics, High Jump Kick, BP, and Swords Dance. The item and corresponding Unburden boost are really quite incidental, honestly, because I find that it's generally better to pass once having gained a boost than to attack. Hawlucha can only ever sweep if the opponent doesn't have a Talonflame or an Aegislash (surely the most ubiquitous of the new Pokemon), a Mamoswine to Ice Shard it, a Sableye to burn it, a Quagsire to wall it, a Klefki to paralyse it, etc. And even then, only if it doesn't suffer so much damage in setting up as to put it within KO range of M-Lucario's Extremespeed/ Bullet Punch, Scizor's Bullet Punch, Megakhan's Fake Out/ Sucker Punch combo, etc. At the same time, none of these Pokemon except Aegislash can safely switch-in on Hawlucha's STAB combo. Hence, I've had the most success with Hawlucha when:
i) I play it as hit-and-run early game and don't force the Dance.
ii) I don't get too attached to Unburden boosts. They're useful but not mandatory for Hawlucha to perform its function.
iii) I pass when I've gotten the boost unless I'm faced with a pHazing wall, in which case I kill it.
That's why I'd stick with encore rather than baton pass (not that I have a choice, since I am playing entirely off the cart and don't have anything to breed baton pass from at the moment). I see Hawlucha as a smash-n-grab. Set it up with unburden and SD, use encore to control the things you don't like (giving you the chance for 2 or even 3 SDs in the process) and go nuts. Then when it's gone, it's gone.
If the opponent has a Talonflame, kill that off first (in 3v3, I leave Hawlucha out of the team if the opponent has a Talonflame). Nothing else I have found to be a guaranteed check against the little fighting bird. The biggest danger is normally a HJK gone wrong.
This works fine on 3v3 on Wifi play (where I've had a fair share of Hawlucha sweeps), but will simply not work in 6v6. Encore can facilitate opportunities for Swords Dance, but in 6v6, every decent opponent is going to have -something- that can come in and either wall or revenge Hawlucha.