I think your best bet would be to treat the area as a shower with a sloped floor, curb, and drain with trap. I suppose you could not even connect the tub to its own drain, and let it use the shower drain. You'd need a tub drain kit to hold the water in and trim out the tub when taking a bath, but just let the outlet dump down to the shower floor and out the shower drain.
The biggest hassle would be cleaning the floor underneath, as there isn't all that much room under a clawfoot tub. Normally, that area isn't designed to get wet or very dirty, and just dusting may suffice. Not true if it is a shower floor. The slope might make shimming the tub a little tricky so it sets evenly, but should be doable.