Thanks!
Cost is not the bottleneck in this case… The problem is that I am rather ignorant about the options and their benefits/limitations. Moving the images the first time was painfully slow because of those same rate limits, and I expect the next migration to be the same, so I want to make a better choice next time and would rather find a solution with the current provider 😅
Good news! Just got a reply from them and they have increased the connection limit. They did not specify what the new number is, but hopefully it is high enough to not be an issue for the foreseeable future.
So, if you do run into other similar reports after this comment I would appreciate it if you tag me again.