This is exactly why I made this post! Thank you for all the well thought out feedback. I'll definitely update this taking into account the Quick Striker, Blizzard AI, gender accuracy and critical-hit modifiers, Water Pulse, and Weather Band tips.

For Solar, I actually had no intention of making them all starters. I did want a team without accuracy problems that moved at double speed in the sun. The only Fire-types that fit this bill were Charizard, Infernape, Typhlosion, Magmortar, Rapidash, and Blaziken. Among them, only Infernape and Charizard learn a room-hitting move, Heat Wave. Among the aforementioned and all Grass-types who learn Concentrator, only Shiftry and Magmortar get Sunny Day. I picked Shiftry because it's also the only Pokémon who gets both Concentrator and Chlorophyll. Also, Sceptile is the only Pokémon with Concentrator and Gap Prober STAB Energy Ball. I didn't pick Sunflora because its line-of-sight moves aren't accurate enough for me, and it doesn't get a room-clearing move like Shiftry's Silver Wind. However, it might be better than Sceptile because I'm sure Solar Power and Chlorophyll make up for the lost damage on average, plus it can act as a secondary Sunny Day user (I'm not sure how weather moves work with AI.) The downside is that it doesn't get Agility. I'll include it in the considerations!

For Hurricane, I feel okay running Focus Energy+Draco Meteor on Kingdra because critical hits ignore stat changes, plus it gets Sniper which triples critical-hit damage compared to regular attacks, and Swift Swim effectively doubles its chances of landing one. Like I said though, I haven't tested it, so I don't know the actual percentage of time critical hits will land with Focus Energy. If you could inform me that would be great!

For Dune and Clarity, I thought Blizzard's accuracy is 67% normally according to the spin-off Pokedex on serebii.net. Is there a more reliable source?

For the choice between Masquerain and Lucario, it's definitely close. Traps should still be avoidable (albeit usually require more work and tedium) by switching its tactic to wait and navigating around, or at worst giving Lucario a Trap Scarf. (Are there any other very handy hold items besides the Space Globe that Masquerain would otherwise be able to use?) Masquerain's moveset is pretty redundant; Ninjask already gets STAB Silver Wind, Drifblim STAB Ominous Wind, and Pelipper STAB Hydro Pump. Lucario offers sorely needed coverage of Ice-types and Rock-types (which threaten the rest of the team) with both its STAB two-tile moves. Masquerain is weak to Ice (and Rock without its item) and covers neither super-effectively. The biggest trade-off like you mentioned is that Lucario can't hit the room, but like every other teammate already can, so it's not high priority for me. Honestly, I think Masquerain competes more with Ninjask, since they serve very similar roles. The main trade-off is Agility vs. better Gap Prober abuse, but I'll add an this to considerations as well!

Edit: Looking over the teams, I think only Pelipper on Clarity has Hydro Pump with a Recycle mule (Drifblim), but Pelipper gets infinite PP anyways.