This is a nutty idea but its all I can think of for now. Take a look at this product, Fast Cap. They came out with these years ago and I have never used them, but I am aware of this product.
http://www.fastcap.com/estore/pc/fastcap-peel-and-stick-cover-caps.asp
Now, like I said, nutty idea but sometimes nutty ideas lead to something good. I told you I would think about your hole problem and I did. I woke up this morning and this idea hit me right away, heck Im typing this at 5:12 AM. What if you were to fill the hole with a wood plug but keep it just below the finished surface (the thickness of the fast cap) then order a sheet of raw maple fast caps in 3/8 diameter to cover the plug. As I said the fast caps can be ordered unfinished giving you the opportunity to match it to your drum wrap. The fast caps come in different sizes. If the holes in the drums are not the correct size for the caps then drill them out a little bigger so they are correct. You get 90 caps for under five bucks so not much of a risk to see how they look. They even sell the fast caps finished and it might match your drum, who knows!
Idea # 2. Use a counter sink,
http://www.bing.com/images/search?q=Counter+sink&id=44269694E9F70AA4CDB7F771B530C3C19EC88F28&FORM=IQFRBA
and wood plug,,
http://www.widgetco.com/5-16-wood-plugs-side-grain-face-grain
Simply but carefully use the counter sink to tapper and size the hole. Pre-finish the plugs and glue them in. It would be ideal if the tapered edge of the plug matches the angle of the counter sink tool. I though of this while digging around for something yesterday in the shop I found a wood plug that comes with hand rail fittings.