Hi Otis,
The right leash for a mat is not an insurmountable goal if a person accepts that compromises in performance will be the result. From an email to a good friend…
Re: drogue questions:
The idea was to slow down the mat if it got away… for both wave and wind action. My goal was to make something compact that had little, or no bouyancy… that would quickly sink, deploy and fill with water, creating just enough weight and drag to slow movement in water and by hard winds. Quick to pull back and place on deck, immediately ready to use again.
Anchor lines were usually between 2’ to 3’ long (longer usually worked better, but were more of a hassle), common supple 1/8" woven nylon cord - like parachute cord. I attached to reinforced front edge lap/grommets, and/or reinforced circular deck patch anchor (homemade)- like those used on inflatable boats, i.e. Zodiac. When not in use, the drogue would (hopefully but not always) lay flat on the deck, forward under chest. Also tried small patches of velcro on forearm or chest to temporarily restrain drogue and keep it from sliding around on deck.
My drogues were crude, sort of like a toy parachute, rear cone section about 12" deep x 6" opening (wire ring). Attached to front close to center. I tried cone, circular, triangular and square shapes. I even tried a 3" hollow rubber ball with a few holes in it (heavy with water, high drag shape) and a small plastic grid cage! ha ha Drogues
which were slightly weighted at opposite end from anchor line, usually deployed the best.
Eventually I got tired of the downsides… getting hit in the face, tangles, no deployment when needed, or unexpected deployment, etc. I have some funny memories : ) Mat surfing drogues are inexpensive little projects to play with… I’ve no doubt you can improve.
Here’s a rough sketch:

One idea I never really tried that might work well and be reasonably safe: a small bag filled with water attached to mat as per previous sketch. Place on deck. Minimal impact risk… fat, baggy, squat shape, larger than eye socket… add/subtract weight while surfing, enough ballast to slow down a mat in water and heavy enough to prevent from
going airborne and flying away. The added deck weight
might even be an asset in choppy conditions. Cheap, easy, low risk 
Hope this was helpful…