I don't seem to have this problem.
I have a similar setup to the original poster (Remstar Auto with integrated humidifier -- I know his is a BiPAP but the setup with the humidifier looks the same) and I just take the distilled water jug (gallon size) and pour it into the humidifier that is still attached to the machine.
I take off a little water on a new jug because the first cup or two is hard to pour -- I pour that into the previous jug. My machine is on the floor on a hard plastic sheet. I sometimes get a little watter in the indentation where the hose attaches to the humidifier, but that doesn't hurt anything.
I put very little water in. If it gets used up and goes dry that is ok, and I don't take the humidifier off very often to clean it. (but that is another thread).
Anyone else like me that just pours? If I do miss a little the hard plastic it is sitting on protects the rug and it will evaporate on its own. Only time I worry is if I slosh any on the machine itself which is rare.