John, I believe you're right - mils means thousandths of an inch. It's how plastic thickness is measured, at least in the US. 2 mils = very thin disposable raincoat, 4 mils=mulch film for gardens, 6-10 mil = heavy duty plastic sheet used as vapor barrier in construction.

I doubt you will be able to get normal Mylar to shrink with heat, I think it's a special formulation. Another common application of the material is in tube form, as insulation for electrical connections - you slip the tube over the connected wires, heat it with a match or soldering iron, and it shrinks tight.

If you're going to go with non-shrink mylar, you'll need to have some mechanical means (tension hoop) to tighten it. This means a rim or "flesh hoop" of some sort around the edge of the head for the tension hoop to bear against. At that point you might as well break down and buy a commercial plastic drum head. I've been round and round this in my head and have always come to the same conclusion.

One more idea just struck me - a temporary tension hoop. I suppose this would properly be called a tensioning jig. Cut two large circles (hoops) out of 3/4" (19.5mm?) plywood, inside diameter just larger than your drum frame, outside diameter a couple of inches more, and one solid disk the same outside diameter. Sandwich the mylar between the hoops and clamp together with a bunch of C-clamps. Leave plenty of slack in the mylar, enough so that you can drop the drumhead over the drum frame and leave enough mylar exposed around the side to tack the mylar to the drum frame. Put the plywood disk under the drum. You can use large C-clamps over the disk and the hoops to pull the skin down tight before you tack it, or long bolts through the disk and hoops. Then remove the jig and trim the excess. Alternative to tacking - rout a shallow groove around the rim and use some kind of band to clamp the drumhead into the groove - maybe a few of the metal band clamps used for clothes dryer vent hose, fastened end to end, would work. Or, what the hey, just get some bailing wire and wrap it around a couple of times and twist it tight. Depends on how primitive you want to be. Good luck.