There may be one on Sentinel Dome as well. I just know that the old lines for AT&T, I guess pre-solar, run down through the area above North Dome. It's kind of on the face and below the dome, facing into the valley, not up high. I found couple coverage maps for Yosemite, but I can't zoom them enough to make them out clearly. I guess you can see if you can make them out, but the red/pink circles showing coverage seem to be emanating from the north rim, so I guess that might stand to reason that there's at least one tower on ND.
Be that as it may, Iridium does do short-term sat phone rentals, and while it's been years since I've bothered, and they are pretty reliable, reasonable cost isn't something I would attribute to it.
I take it the Mrs wants you to stay in touch? That's the "I'm ok" beauty of the In-reach. With me and mine, it was always that the worry should begin when a call comes, and if that doesn't happen, assume we're fine. I know how it goes though.