GRABAAWR first timer here also, although I've done a couple of other tours. Same concern about getting in the miles because of the crummy weather (had a little frost this am and a temp at my house of 34F.
Don't know how far "up north" you are referring to, but in WI, snow is long gone, so the mighty Miss should have received this runoff by now. Not an expert by any means, but I would think the WI river will be OK, unless of course we have a monsoon from now until the ride, then who knows.
I'll be riding in my first GRABAAWR this June. I'll be driving up from St Lous. A bit worried about my ability to do this as I'm way behind on my riding due to the weather. We're all anxiously awaiting the snow melt up north as our "normal" Spring flooding will begin then -- on top of what is already happening. Any concerns on the Wisconsin River that might affect the bike ride?