I also run synthetic fluid in my transmission and in the differentials. Be sure to check the owners manuals as some differentials require the addition of a small amount of limited slip additive available at most automotive stores. You mention going up and have considered many of the concerns there, but don't forget the coming down part. Most of the energy used in going up needs to be handled when you come down. Be sure to check the braking system and possibly swap out the brake pads for High temp/ heavy duty ones.
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