Dave,
I've got the same cupboard.. i.e. the water, one could always plumb hot water to it. We plumbed a toilet to hot water by mistake in the bunkhouse at the hunting ranch in NM. Funny thing was, everyone complained the next year after we had re plumbed it...
Seriously, was only trying to show an example of an alternative approach. We've got a Toto unit in the stick house and I'm waiting for DW to ask for one in the RV..
Steve