I once checked with UPS and FedEx and both would have been well over $200 but would have delivered in 2-3 days. USPS says 7-10 days but usually does a little better than that. I have heard that some people love DHL and others.
The game board box will easily hold 2 keyboards, maybe even 3 if they were thin, as long as they were not in bulky original boxes of their own. I have a Leopold in a svelte original box from Elite and I know that 2 of those would fit.
A single keyboard (but not a monster Model M/F 122-key terminal board like I am using now) via Priority Mail will go a little cheaper on a short run, say $30-35 for East Coast-to-England, but I doubt that you will do significantly better otherwise.