Fees can be capped by offering a settlement. The court will not allow you to ignore a reasonable settlement and then charge fees for work done after. “Reasonable” is defined by a better or similar outcome to what you got in the end by continuing litigation.

What about capping fees at whatever the party having to pay spent on their legal team, so the party choosing to pay more expensive lawyers for more hours is taking the risk on that increased cost vs. the other, and the less you spend on your side the less you're liable to pay if you lose?