Our local rental house has a motorized scraper that vibrates a knife under the flooring. I have never used one, but the shop owner says it works great on 12x12 inch vinyl tyle, but not quite as well on vinyl sheet stock. The rental cost is $27 per 3 hr minimum. I suspect that since your flooring glue is new, it may be harder to remove the flooring (the glue won't be hard and brittle) KD may have the best suggestion, just put the backer board and tile over the vinyl. Good Luck!