You could try a toe-kick saw. See the link below.

Are you sure that's paneling under the vinyl vs subflooring over the plywood?

Here is a link that might be useful: saw

Yeah, that's subfloor under there.

Um..not really into buying a new saw to get this done..esp. one that costs $260! Can't find a rental either.

I'm going to try to cut away the vinyl. Then I'm going to seriously score the subfloor and try to snap it clean against the toekick.

When you say "paneling" I'm thinking it's actually 1/4" plywood of some kind. A really sharp utility knife will cut it; just be really careful; wear gloves. A Japanese-type "pull saw" would perhaps also be useful if you got one that cuts flush without the handle in the way. Expect to pay about $25. for one. If it hits a nail or staple it will soon be toast. The knife will do the job.
Casey

This panel/subfloor whathaveyou has a name...I just can't think of it.. Anyway, yes, it's thin enough to snap-probably about 1/4" thick. I've taken a hammer to the back of an utility knife (at the best angle I can under the toekick) and I have gotten an okay edge, but nothing great. I've gotten a very important part done, but might wait for the floor installers to take a look and see if they have a suggestion/tool.

If they can't halp me out, I'll try that little hand saw.

"Um..not really into buying a new saw to get this done..esp. one that costs $260!"

By the saw, use it, then sell it on e-bay.

You will likely get at least half the cost.

It's probably 1/4" Luan plywood under the vinyl.