you can get spray on glue but i aint sure how good it is, if you drill small holes in the strengthening supports you can use lengths of thin steel bar to hold it in place, failing that, i aint got a clue
What about contact adhesive, or I know for a fact that the proper stuff for sticking down hardwood floors has superb stickability a local to you flooring firm may have a small amount left over from a job because it's quite expensive to buy a whole tub. Hope this gives you some ideas