tl;dr - Advanced Renamer is free and phenomenal.
I haven't tried in Cygwin or command prompt for file conversion on Windows yet but I've been using Advanced Renamer for many years now and have been very happy. In fact, next paycheck I think I'll buy a personal license because it's been so great and I'm happy to support it since it's saved me tons of time and effort. It does have a file limit cap (I think 10,000, but I'd have to double check) for each operation, but that's pretty high and I rarely need that many. Also, you could just run it several times on larger groups broken into subsets.
It has a pretty straightforward interface and is a very very powerful tool.