Never done this before because I run a welded hull. Because I am a do it yourselfer I don't think it would be all that difficult. But obviously not my boat.....
I would pick a seam that is easily accessible and monitored and try adding a rivet on either side of ones that you notice being loose. The thing that I see being the BIGGEST problem is how to tighten the seams. I would imagine that the flexing hull has wallowed the existing rivet holes a little and allows the seam to flex a little each wave. The new rivets would only prevent the issue getting worse and possibly tightening the problem seam a little.
Watch them closely.
I spoke with a guy on Mac a few weeks ago that has an old wood Chris-Craft that he has to fill with water for a month each spring to allow the wood to swell and make it water tight. So just maybe you could use caulking on each seam prior to installing new rivets.
I see this being a very costly repair, plus your timing sucks. Any shop worth getting this done is going to have a hard time setting aside a week for your repair.
There was an informercial of Billy (someone) spraying a substance on a screen and then magically a day later using it as a boat. lol