Here's a possible finagle:
You might be able to rig up something using one of the self-straining litterboxes which has 2 pans and a strainer. Or use some plastic screening from a hardware store and 2 pans..
Place some sort of blocks under the strainer section to accomodate the "urine lake" or use an absorbent pad on the bottom to soak up said lake - you may be replacing these daily, though.
Use crystal type litter - the urine drips right down, only the feces are on top of the crystals and must be scooped out. Sift it in the strainer or screen first and dispose of any dust or small particles, so they won't wind up going down the toilet or drain.
When cleaning the box, lift the strainer out and move it over to the other pan; you may want to rinse it first.
Drain, clean, and dry the used pan for the next day.
Repeat as needed.