Overflow clearance problem

[MikeM]

I am installing a new drop-in type tub with a side drain. The tub edge is 3-1/2" wide and 1-1/2" high with a wall thickness of approximately 3/16" - 5/16". I am mounting the tub filler and handles on the tub edge rather than on the tile deck. I already cut the holes in the tub for the valve assembly and was all set to sweat everything to the supply when I realized I hadn't considered the overflow drain assembly. I don't have enough clearance for both the valve and the overflow. Is there a super-low-profile overflow assembly available? Can I do without the overflow? I know it's not a good idea but it seems the simplest solution. If I can do without it how do I close it off? So far, this has been the only chink in the armour...and it's a doozie.