I had the same thing happen on a late season Lodore trip last year, where the system dropped my group size to 1 person. I eventually got someone on the phone at rec.gov who was clueless and unhelpful. One thing you might try is to go back on rec.gov to see if you can change your group size yourself and reprint your permit with the correct group number (this might not work since you've already printed your permit out).
As far as the Salt, we just got back from our trip last week. At the road down to the put-in I was asked by the Tribal Police to produce my river permit and adjoining permits to both camp at the put-in and for the first 2 nights on the reservation. My group size wasn't checked at all as the rest of the group met up later without producing any paperwork. I think this process is really hit and miss. We didn't see any other ranger/park employee for the entire trip. No one checked us out at the put in at all. I would highly suggest that you not play around with the Tribal Permits. Get them online, it's an easy process, $25 per person per day on the river, and $15 per person to camp at the put-in.
I think the tribal police are most concerned re their use permit, not the river permit. If it were me I'd try to call Rec.gov to address this and I'd try to see if I could fix it myself online.
I can't guarantee that you'll have the same experience but I wouldn't sweat it at all, just tell your group to meet at the put in and make sure they all by their tribal permits. I'd be shocked if you have anyone look at your group size/permit.
I continue to think that Rec.gov is a mess and look back fondly on the days we didn't get our permits from that system.
Have fun! That is a really great float!!!