I'm afraid I don't know of an integrated in that price range with tone controls. Paul's suggestion sounds the best to me as you keep your current integrated amp and the tone controls are completely switched out of the audio path when you don't need them.
It's funny though, since I got new speakers I'm starting to appreciate how well some of my 50s and 60s albums were recorded. The engineers had fewer toys at their disposal and it would appear that this was a good thing.
