Edge Tarnish On Silver Eagles

acetone, will not do anything to remove toning..

The coins have most probably acquired their edge tarnish in the edge milling by handling them only by the edge, as you should do.
Perhaps a good reason why gloves should be used, especially when handling modern proof coins

I have to admit: I don't bother with gloves, but then again, I don't collect modern proof Mint product.

Good quality coin albums are made from acid free materials. So normally, the coin album is not the culprit for tarnishing.

Unfortunately, the tarnish is most probably caused the acidic natural skin oils in the fingers. The tarnish is permanent, and cannot be removed without damaging the coin. The black stuff is a silver oxide/sulfide complex salt, that is now part of the surface of the coin. That being the case, a soak in acetone won't be of much help.
That is why some collectors prefer to use gloves when handling coins.

@kiteray: When you say "uncirculated" are you referring to the regular bullion coin or the special collector version sold by the US Mint directly to collectors w/o a middle-man?

If your coins are the bullion versions, a single, quick dip and swish (1 to 3 seconds) in Jewel-luster will not harm their value as their value will always be driven by their weight as silver bullion. The bath in this solution should get rid of all/most of the toning you are seeing. DO NOT over dip as that will remove the coin's luster and make it far less attractive!

If your coins are the limited edition collector versions, it might be best to leave them be.