First off, thanks to everyone for the quick and informative replies. I'm grateful for your help.
This job post for a backcountry guide was put up May 10, two days ago, which hopefully means that it's still open, but I'll follow your advice, CalicoPenn, and I'll definitely call Monday morning to confirm.
Regrettably, I don't have a scouting background. Like I said before, my brother was a Scout and I hung around some of his events growing up. Two of my best friends are Eagle Scouts, though I don't know how official their recommendation would be. I'm at least fairly familiar with the organization and how it operates, along with things like Leave No Trace, even though I'm not certified at the moment.
I'm actually getting my lifeguard recertification next week, which includes CPR. I've taught swim camp every summer since I started working, so I have some familiarity with responsibility and teaching kids. I camp, canoe, and hike, and though it's only for personal recreation, I do have some experience there. I wouldn't apply for a job with this responsibility if I didn't think I could handle it, but I do recognize your concerns. I definitely wouldn't want to see an inexperienced guide with the potential to cause problems in a position of leadership.
The website says that they do provide all training and certifications for the position on site, including Wilderness First-Aid, Lifeguarding, and LNT. I know enthusiasm doesn't make up for lack of experience, but I can get experience through working. Enthusiasm is a little harder to develop. I think I have the energy and willingness to learn that would make the summer a great one. Cito, I'll take you up on that advice and put in for a Philmont job as well when they have a position open.
Once again, thanks to everyone for your help!