Just thought I'd follow up with our experience. We managed to fit all ski gear in two carry on size suitcases, and just our boots in boot bags fit easily in the personal item sizer.

We did not have to size our bags boarding the plane at MSP, and I'm not sure they used/cared about the boarding pass stamp at all. We did have to size both and get our boarding pass stamped at our connection in DEN, though this process was started long before boarding, so there was plenty of time to size bags without holding up the boarding process. When we checked in at SLC for our connecting flight home, the attendant at the ticket counter stamped both of our boarding passes all the way through without having us put our bags in the sizer. So over a total of 4 flight segments, we only had to size our bags once.

All flights were on time except our last segment going home (due to a delayed incoming plane), so making the tight outgoing connection was not an issue at all.