Check to see if the transformer of the amp is easily rewired for 110 volts. Most are. Sometimes it is as easy as moving a jumper plug.
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With the current exchange rate, things are fairly competitive priced in the US, since many manufactures have not adjusted their prices.
An exchange might be more interesting as well: A chance to try new things...
The step-up will work here without problems. You will need a fairly big one, >1000W. If you are lucky you might find one for less than $100. Also, the additional transformer might work as additional isolation transformer and get rid of some AC noise. However, all the step-up transformers I used did have slight humming noise. Best to place the step-ups out of sight.
Also, it might be worth checking on whether your amp can be switched in voltage by a simple switch, resoldering, or a transformer change.
A fellow European with similar problems.
You can have an electrician instal a 220v dedicated outlet for your amp. It will have two 110V lines (hot) and a grounded neutral. This will give you the sonic benefit of a balanced power. This is how a PS Audio Power Plant works on 120V equipment, two 60V lines and a grounded neutral. All of my Linn gear is running that way (220V). Hope this will help. Hector