<< Is there a fast way to get all the dreck off? >>
Here's a couple things that worked for me:
Used my router with a bit that had bottom cutting capability and set it to just
touch floor level. Swept it back and forth over the lumpy stuf with a shop vac
handy and it cleaned off the lumps pretty quickly.
Another job with soft gloppy stuff was removed (but somewhat slowly) by one of
the 3M adhesive removers. They have several that work well without attacking
automotive plastics, finshes and such, so the vinyl was spared in that case.
There are other commercial removers that might work, such as Goof-off. Head for
your Ace hardware and spend some time reading labels and odds are you'll find
something that will save you time and effort. Good luck.