The 10-22 on an APS-C crop body is an absolute gem, and is a lens you'll use a lot on your trip.
15mm sounds wide, but do the sum; 15 X 1.6 = 24. Hmmm not so wide.
The 10-22 is a hero lens in the EF-S lineup and would be very quick to sell on Craigslist if you transition to FF at some time in the future.
Paul Wright