Hey, what about mesh? Like drywall mesh. You could use it as a substrate under the wide piece and the strip as a way to bridge them together with glue (epoxy?). It’s thin and strong and would allow a thin layer of epoxy to bind into the mesh and onto the bottom of the LVP. Since you’re really just using it to stabilize the floating piece, it doesn’t have to be super strong…especially if it’s got a fair amount of surface area compared to the strip.
You might have to test it out to see if it adds any appreciable thickness. If it does, could you maybe grind down just a little bit of the subfloor to allow for it?
Ryan/// ~sigh~ I blew up another bowl. Moke told me "I made the inside bigger than the outside".