pdh:
Here's a sketch of what I suggested earlier - epoxy & ply solution.
...
If it were me - I'd go to Burnsco and buy the smallest kit of WEST epoxy (2-parts - resin & slow hardener) and a small jug/bag of thickener powder. There are other brands of epoxy - I just like WEST and have used it for 40+ years. It's never let me down.
You can get small kits of Norski 'Epoxy Glue' at M10. About $25. It's a pre-thickened two-part epoxy.
Just be aware that cured epoxy is rigid. If your floorboards are exposed to significant changes in humidity they may contract and expand across the board, while remaining relatively stable along the board. Ideally this movement would be absorbed by the tongue and groove. If excessive movement occurs, you don't have any mechanical support for your infill panels. Just the adhesive.

