Hartford Athletic. I see the traditional wage budget which you can technically raise by transferring transfer budget over, but I assume this will be enforced when registering players for the league.
I ended up freeing up over $1.1 Million in the wage budget (only 600K on the books), and still couldn't offer more than $14.75K a year, so clearly something is amiss. I did a few test saves in other leagues after this and haven't had any problems. I couldn't see anything particularly out of whack when looking at the club in the editor (having loaded your file) and the club finances were fine, nothing looked wrong when checking the club with the in-game editor either.
The only small detail that may have looked odd was when I looked at contract types for USLC (Star player, Important, etc...) they didn't have a categorization (full time, part time, amateur, etc...). Not sure if that has any impact. I also used the "Real World" setting when trying this save, not sure if that might've thrown a wrench in the works.
Also thanks again for all the hard work you've put into this, I don't want to sound like I'm complaining one bit. I've never run into this issue before in 20 years of FM, so I'm trying to get the bottom of it.
EDIT: Tested this using the original game mode, still have the same problem. So it isn't a problem with future transfers coming in and out.