Your Fein Multimaster is exactly what I had in mind if it is necessary to cut the subflooring off flush with the walls. I have the cheap Harbor Freight knock-off, which does a surprisingly good job of flush and plunge cuts, but the blades are not hardened and don’t last real long. There is a specialty flush-cutting circular saw which is used by flooring professionals. Possibly you could rent one for your project. It would be much faster than the Multimaster.