Robyn,
This is not a method I would suggest normally but I have seen it done. It will certainly impact the tone of the drum but I am also aware that you prefer a pretty heavily muted sound.
I knew a drummer that used to wrap his drums in polyester (spandex). When I say he wrapped them what he did was basically make a "bottle cozy" for each drum. He then removed the hardware and stretched the fabric "tube" over each shell. I think this included the bearing edges so that the elastic ends fell inside the drum. I am not sure how he did the holes for his hardware but I suspect it involved a soldering iron to weld the edges of the holes. He re-finished his five piece kit every so often as he said it was a pretty quick process. It was funny to see what color kit he would have next. The polyester lays very flat as you can imagine and yet it has a bit of a natural sheen so there would be no need to clear coat it.
Again, I am sure this will have a negative impact on your drum sound but if this kit is for your own enjoyment at home you may actually like the additional muting. No glue, no mess. Just a thought. It is also VERY reversible.