In order to get it to sound good, you have to do what needs to be with all snares with old heads - give them all new heads and a good set of wires............
It may turn out to sound great once that is done - but you can't give it a fair shot until you replace the old worn out consumables. I recommend the standard Remo Coated Amb and the Amb snare bottom - and some of those Puresound Knock-off German made wires sold by drumfactorydirect. (Or just some Puresounds)......Yes, as you likely know most of this.....good wires make a significant difference.
I had an old Pearl made that I had some double 45s cut on - top and bottom - and the snare just came to life and became the best snare I had at the time.
I would not hesitate to cut the edges on that - risk/investment is low. I would even do it myself if I were you (if you have a router/router table) Even if you have no table I have seen people mount their router on a board (plenty big) and then cut by moving the table/router around the shell instead of the shell around the router/table.