I took a trip to Belize a while back, had my 10D here are some of my photos. Check the focal lengths. You will want a wide lens, on a crop sensor definitely coverage from about 17mm-70mm for most shots. I wish I had taken a macro lens for the flowers but used longer glass for flower and butterfly.
When I went my widest lens was 19mm..
17-40 f4 or your 17-70 and 70-200 f4 would be ideal, low on weight and great coverage for 90% of the situations you will encounter. Take a polarizing filter and neutral density filters for waterfalls.
You will experience very high humidity, do the bag trick with your gear when coming out of the A/C till your gear temp stabilizes.
I have a Sigma 30/1.4 but don't find much use for it while traveling--I just use a 2.8 zoom instead. If you don't like the CA on your Sigma zoom, you may dislike the 30/1.4, my copy has a fair amount of CA, but not sure how it compares to the Canon primes or your zoom.
I am sure others will chime in that have had more recent experiences, and I hope they do. I am no stranger to traveling in Central and South America. I've been to Belize, Guatemala, Mexico, Ecuador, Peru, Costa Rica, Panama and Brazil. In fact, I am building a house in Ecuador right now. By far, Belize was the one country were I felt the least safe, and I will never go back. My worst experiences were in Belize City (the safety of myself/wife threatened unless I paid $20), but everywhere else was in the country was fine. Except for one incident in Placencia where I was awoken in the middle of the night in the back of a rented Suburban - approx 8 people (4 on each side) were outside rocking it side to side trying to tip it over. Now having said all that, I traveled there in 1990, so things may be better. I say this because based on my experience I would not travel there with expensive camera equipment. I would hope things have changed. The island people of Ambergris Caye were great, and very friendly. I would stay away form Belize City.
