If we want a Pokemon that works well, we can't just throw together a bunch of independently-reliable traits and hope they magically turn into a Sand savior. We know our purpose because of the topic; we know the direction we're going to take because of the established ability. Things like Sand Rush don't work because that's not what our Pokemon was designed to do- our Pokemon is supposed to act as a check / switch in to a bunch of threats, and it's already been established by multiple arguments that at least some adequate amount of defense is required. I don't want to put things like Soundproof on this Pokemon because it's purpose isn't to counter as many things for Sand as it can- it's purpose is to counter a few relevant things, but counter them well, and without a Fairy resistant typing or a Fairy countering STAB, it won't be able to do that, even with Soundproof.
The ideal final product imo is a semi-tankish one that leans neither on attack or special attack but is not weak on either. Speed is not necessarily a necessity because most of the things we're trying to beat will outspeed us unless we invest an insane amount of stat into its Speed, which is a waste. I'd rather have something that can sponge a few neutral hits and then rely on the super effective power boost to make up for an unoutstanding offensive lineup.
Thus I suggest CONTRARY.
Against Intimidate:
The physical side of Contrary gives this Pokemon the ability fuck up Intimidate users real good, mainly Landorus-T, Mawile, Hitmontop, and Mega Manectric. Really only Mega Manectric has but a small chance to OHKO you- with HP Ice- but depending on the amount of defenses we choose to give it, it could be used to check one of the most popular Rain Mega Pokemon as well. They'll find it tough to switch in, as they'll only continue to boost up your power. This will also allow this Pokemon to be stellar as a lead, scaring off opposing Intimidate leads and preventing lead Manectric from Mega Evolving so soon.
Also, it can be used cleverly in double switches, especially if Sand is up and you know a Landorus is going to switch into your Excadrill- since you can switch first, you're pretty much safe to come in and grab that boost, wasting the opponent's Landorus switchin and also grabbing some momentum in the process.
Against most other threats:
The main reason why I like Contrary is because it gives this Pokemon a lot of tankish ability without forcing us to invest too much in its stats or restricting it to one offensive type like Defiant or Competitive. Depending on the opponent's lineup, you'll have power when you need it (ie to muscle past Intimidate) or just bulk if you need to stall things out. Stat-breaking in order to try to muscle past you (ie with Shaymin-S or something like that) won't work either, though it would be stupid of your opponent to try. But you never know.
Another great thing about Contrary is that it opens up a lot of powerful moves to this Pokemon's arsenal. Obviously we'd want two strong, reliable STABs for this Pokemon, which shouldn't be hard to find since Grass / Ground has a lot to work with. However, in terms of coverage, Contrary makes a lot of coverage moves a lot more viable as well, and can even help this Pokemon set up without having to forfeit offensive momentum. Defiant and Competitive don't offer this - if you use Leaf Storm, your Special Attack will still plummet. With Contrary, moves that have drawbacks will become benefits, not only adding to this Pokemon's power but also to its stay in ability, as it won't have to switch out as often.