But the main thing that I find intriguing is the Legendary Raids. I really wonder how those will work in terms of actually catching the Pokemon in question in Crown Tundra. Legendaries tend to have notoriously low catch rates, and Raids only give you one shot at capturing the Pokemon until they escape. If they keep their catch rates at 3 then catching them would be nigh impossible. Assuming they are catchable in the raid, maybe it'll be like LGPE where you have to thoroughly defeat them before being able to capture them? And maybe the catch rate will be higher than in past games. Or something like that, or something like the recent Zeraora event where they will be distributed if enough people defeat them? The latter is something I'd rather not see tbh but we'll see what happens. I really do wonder how the Max Raid cover legendaries and vice versa will be catchable despite only being seen via Raids.
Well, one issue they need to work around is that they're going to have to find a way to prevent players from getting multiples of the same Legendary but not lock players out from helping someone looking for that Legendary.
If I was working on it, I'd probably do your latter suggestion and go the LGPE route. First you battle the Den Boss (be it Legendary or otherwise) in a battle where you just got to defeat it (like with Mewtwo and Zeraora) . After beating it you then enter a LGPE-style catching screen where you have a few minutes to chuck Poke Balls at the Legendary trying to catch it (I'd also increase its Catch Rate so it doesn't take 10+ high modifier Poke Balls). If it's a Legendary, while obviously the player that started the Raid will then be given a chance to catch it, but for everyone else I can imagine a few things. I would like it is if you don't have the Legendary as well you also get a chance to catch it while those who did instead get to catch a certain Shiny Pokemon (mostly normal Shiny but if you're lucky it'll be rare Shiny-
WHY DID THEY ADD AN ADDITIONAL RARITY TO SHINY POKEMON?!). However I wouldn't be surprised if those who joined in on the Raid only get to try and catch another Pokemon (and maybe it'll be Shiny). Obviously the worst case scenario is that after you defeat the Den Boss and get the item rewards you're just kicked out, no Pokemon to show for your efforts.
I say Den Boss as I'm going to guess not every Den Exploration is going to end in a Legendary encounter. If you still have a Legendary to get it'll probably be an increased chance, but like with the USUM's Ultra Wormhole Ride you know they just can't make finding a Legendary and catching it straight forward.
And if cover legendaries will spawn more than once if they fail to be caught.
I imagine if you lose the Raid you're kicked out (or, if they do the LGPE timed catch mode, run away) and have to find that Legendary's Den again. A pseudo combination of not losing the chance to catch the Legendary but also having that feeling of "this is my chance!".