Quick update: Talked to the parents again, and after explaining how I had planned out the trip so far (stopping at key points along the way, making sure I'll have enough water, staying close to civilization when possible) they still seem a little skeptical, but more accepting than before. So that's good?
Still haven't managed the trip to Lander (school/work getting in the way) but I did just over 20 miles two days ago with zero issues. Legs were quite sore the next day, but what else was I expecting? haha