What condition is the original floor in? If it's in decent shape I would
be
very hesitant to cover it at all, or at least to permanently marr it up.

The floor is kind of marred up already. I removed the old tile and
1/4" plywood that was on it originally. Structurally its fine.
We have oak floors throughout the first floor, but we liked it better
to have tile in this entryway because it was easier to clean plus the
tile floor continued into the kitchen, which I am remodeling.

I'd just sand the finish rough, seal it (in case any water gets under there)
and just tile on top. Sounds like you have a secure base already... But I'm
just a handyman, so take my comments with a pinch o' salt!