I have full XT mtn bike gearing with an 11-34 cassette on my LHT. I live in Colorado. We have a few hills here. If you are going to do any climbing at all on a loaded bike, I recommend a mtn bike crankset with a 22-tooth chainring. I have used my lowest gears (22-34) many, many times, and not just on Red Mountain Pass (~11,000ft). My loaded bike weighs 75-80lbs. (I only weigh 110lbs.)
Some friends of ours just got complete LHT bikes and the Boy is helping them build them up. Then the Boy decided he wanted a complete LHT, so he ordered one. He swapped out a lot of parts and now has a full XT mtn bike set up on his too.
Happy to answer any LHT questions you have. Got 4 of them on hand here!
FWIW, I will be riding Wolf Creek Pass this June in the Bicycle Tour of Colorado (7 day road bike supported tour). We'll be riding it from Pagosa Springs. I've driven it in my car. It's a freakin' wall! gah. I have an 11-34 cassette on my road bike too! My low gear on it is a 30-34.
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