I never updated this thread. When we got to the airport I went to the Skypriority check-in area and asked the agent to reprint the boarding passes with SP on them.

At first he didn't seem to be keen to do it, but I pointed out that we were all on the same reservation and offered to show him the receipts on my phone, so he did some magic on his terminal and gave us 6 BPs with SP on them.

I don't really know what was wrong (the line behind me was getting longer quickly), but I think the main takeaway is that a check-in agent can override whatever limitation and add SP to a boarding pass.