I have used the following method to attach such articals that can't be glued safely.
Build a platform out of foam core for the buckel about a quarter inch smaller than the buckle. You may have to use 2 thinkness's to be deep enough for your 3/8 inch debth on the underside of the buckel.
Now attach the platform to your mats with wire, fishing line, or Attach-EZ. You can glue it down for extra reinforcement as well.
Then use 3M's Dual Lock. This can be attached to the platform at the same time as attaching the platform to the mat. Attach the looped side to the platform (it is very sticky, but for extra hold I would reinforce it by using fishing line, wire, etc).
Now attach the other half of the Dual Lock to the inside of the belt buckel. Dual Lock works like very strong velcro. You may want to use a small amount of silicone to hold the dual lock on to the buckel as well. In this way you can make the buckle look like it is floating without anything holding it in place.