By "neutral-element", I'm including same-element too. Mordred becomes all the more important though.

I keep Gaia in reserve in my team, since it already has Sol. 2 off-element reduces damage too much; even if it works, it's just way too slow. Having her in reserve also keeps her from getting killed by triple attacks. She can be used off-element in the main team also, so long as she's the only one. My Water team has -50% ATK and high HP, so it usually takes 2 overdrive hits to kill a character. Losing 3 characters at once is extremely rare; my team will remain full-power so long as 2 or less are killed by the first Raging Overdrive. Strong Wind teams with at least Awakened Gaia and Oberon should have no real issue with Accessory Quests, other than Fire.

By "maxed" team, I'm assuming 42k+ team attack power and >+100% character attack power from weapon skills, as well as >80% elemental attack power from eidolons. That's assuming a full grid of maxed level and maxed skill level same-element SSRs, SR+ Assault, and of course eidolons. It's likely possible to do with less, but I already lose occasionally as it is. If you're going to waste all those resources on the entrance fee, you want to make sure you're going to win. Otherwise, you should just do Rank 3.