I would like to thank everyone for their suggestions. It turns out the
surface was MDF, judging by the amount of smelly, noxious dust produced
when I tried sanding it off with an angle grinder.

I gave up on the goal of keeping the level the same, and opted to put
down additional 1/4" plywood using screws and yellow glue. The building
supplies store manager gave the materials for free when I told him how
I was sold the wrong type of plywood, so I'll just chalk it up to yet
another bitter experience.

Thanks again,

_ Gord