Ubers and UU should definately be considered, wouldn't the Smogon Tour revert to different generations (RBY, GSC, RSE, DPP) once available anyway?
Battle Pike: Luck Symbol
I believe this one should just be a regular OU battle, with a slight twist. Freeze Clause, OHKO Clause, and Evasion Clause should all be un-checked. Adding more of an element of "luck" to the battle. (I'd still be a bit weary on turning Sleep Clause off though, but if that seems fairer then so be it).
Battle Arena: Guts Symbol
This one could be a little more difficult. In the game, you play one Pokémon against your opponents for three turns without switching, and you're judged on three different aspects, which will probably be too hard to do over Shoddy Battle. In the anime, a randomizer chooses whether the battle will be 1vs1, 2vs2, or 3vs3. Now, we could replicate this with the Brain asking a challenger to pick "A, B, or C" and have all three randomized. However, playing 1vs1 is heavily reliant on luck as well. But we could still do this, maybe change it to 2vs2, 4vs4, or 6vs6, possibly even implement a best 2/3 basis on this as well.
Battle Factory: Knowledge Symbol & Factory Medal(?)
Will obviously be similar, but we can just play around with these. You can still add a lot of clauses to a Random Battle, so having slightly different ones for each is probably enough. One could be best 2/3, one cold be best 3/5 or whatever...
Battle Dome: Tactics Symbol
No idea for this one, would probably be best off just switching the metagame to change the "tactics". Probably UU.
Battle Pyramid: Brave Symbol
No real idea again, but I'd just say this one should be Ubers.
Battle Palace: Spirits Symbol
No idea...
Battle Tower: Ability Symbol & Tower Medal(?)
We usually judge ability primarily on the Standard OU Metagame, so I think the Battle Tower(s) should be simply OU.
Battle Roulette: Roulette Medal(?)
No idea... Probably Little Cup though.
Battle Castle: Castle Medal(?)
No idea...
Battle Stage: Stage Medal(?)
Was thinking potentially mono-type, but not sure.
It could be problematic getting Brains to agree to rule-sets like this though, because I know I'd only really want to go for OU at the moment. But there's good variation there...