[Stiglr]

A quick primer on how I might see it progressing...

Start with a large, thin cylinder. Do some thinking and some math to set the number of the cylinder sides to help you when creating the undulating outer rim. This, more than anything else, will save you a bunch of time.
Place a cut near the bottom on the outside (either that or form the cylinder to have two segments, then move the vertices of the center line downward to create the thin lip; then perhaps combine the lip faces on the inside of the snare).
Extrude the outward edge to form the flange.
Make a set of additional cuts, in a systematic, symmetrical fashion to create the edges tuning flanges. These may or may not need a lot of cuts to form the rounded edges to the flanges, or you could decide to leave them more sharper edged. The more gradual the edges, the more cuts you'll need to make, and the more complicated it will be.

After segmenting the flanges, you'll need to select either edges or vertices in groups and move them up or down all at the same time to create the tuning hole areas. This will probably involve moving some of the outer vertices/surfaces to create the effect.

I can explain a better way to make the tuning holes themselves without using boolean cuts (which would create an entirely new mess!) Basically, I'd use Make Hole in each of the raised areas of the flange, and use a disc as a "tracing template" to align the vertices of the hole, adding/subtracing vertices to duplicate the number of vertices in the template disc. (Better explained while sharing a screen; this is hard to describe in text).

Again, PM me and we can arrange a time to meet over Skype (if you don't have Skype, just get it! It's free and easy to install and use... hopefully you have a headphone set or a mic in a laptop so that you can easily use it to teleconference.