Yeah, I definitely feel for you. Rototilling might make it worse if it's too wet. Whenever we would drag the arena with the tractor when it was too wet, it'd be deep, thick, sticky mud and we'd end up with huge clods when it dried. That's if your rototiller can even till through it. We dug a lot of drainage ditches to drain water away from stalls, walkways and riding areas. when it was dry enough, usually earlier in the year, we'd spend a lot of time making sure stalls were even (no dips or holes) with a slight grade so it would drain well. Sometimes that did involve tilling up the whole stall, raking and leveling, and then tamping down with a dirt tamper.
If you can afford it, I think mats would be the way to go. They have mats in all the stalls at my barn in Northern Ca. (where I now live) and it is SO so nice. We don't have DG but we have an overabundance of rain and they help a lot in the stalls.