I was thinking along the same line - perhaps a ramp up to the counter and you could leave the water running at a slow trickle without running up your water bill. My son has a perfectly healthy cat, who over the past year has refused to drink from any bowls, etc., and will only drink from the bathroom tap, and she has 3 baths and the kitchen to choose from but will only drink from the same one all the time, so the water stays on at a trickle all the time. Finicky cat - go figure!!!
Hope you can find a solution soon - I know you must be getting frantic with all that is happening.