Mystery 1940’s Flooring Texhnique Uncovered

[Mprince106208]

I’m in the process of remodeling our 1949 master bath. After demo and removal of the original tile floor, wire mesh and cement, this is what’s left. 2 x 6 floor joists carved to a point with support rails for the floor boards.

How should I build on top? Or remove completely and start over?

Any help would be very much appreciated!

Matt