extending hearth tile over wood floor

Queso Bandit

I just bought a fireplace insert and need to extend the masonry hearth by about 2 inches to achieve the 16" code requirement.
The existing hearth is about 3/8 inch higher than the wood T&G floor, with no subfloor (cheap 1942 construction).
I'm planning to install 12" x 12" slate, so only about 2" will be over the wood with the other 10" of tile supported with solid brick below..

Is it ok to just build up thinset at this 2" extension area and tile directly over the wood? Should felt paper/ some other membrane separate the wood floor and thinset?
Would a 2" strip of backer board help anything? It wouldn't lay exactly flush with the existing brick.

Thanks in advance for any advice.