Pressure sensitive adhesive-type hook/loop fastener should not be trusted to hold anything under any amount of stress. In this case the stress would be gravity, and it works every minute of every day, 24/7/365.
3M Dual-Lock would be a better fastening technology for this purpose, because it is more durable than typical hool/loop fastener. That said, problems usually are not associated with the fastener, but with the pressure sensitive adhesive. Some hook/loop fastener products are available with a high-quality acrylic adhesive, which would be better, but still too risky as far as I'm concerned. The bond depends not only on the adhesive, but both of the surfaces joined, and its adhesion to them. Too many variables, too few choices, too many failures!
If the plywood is thick enough to allow screwing through the floater and a spacer-layer, then that is what I would do...carefully; with pre-drilled holes and screws of precisely-selected length.
If the plywood is too thin for screws, then I might consider using non-adhesive Dual-Lock (or hook/loop) fastener, attached by acrylic gel as David suggested, or by Lascaux 360 conservation-quality contact adhesive, which is nothing like hardware store contact adhesives. Lascaux is strong, yet chemically stable and removable by a conservator using certain solvents.