running games on old storage devices that hold less than 32 GB and have terrible read and write speeds.
I'm confused. How about copying that to newer storage devices?
Also typically game assets are VERY well compressed so I would suggest doing a comparison with/without compression before a full on migration. Compression tools help but aren't magical. If your assets are e.g. .jpg or .mp4 or .mp3 or a combination of that (as typically game assets are, including 3D models with their textures) then you can test yourself to .zip them (or bzip2 or whatever you prefer) and you will seem some gains but they'll be nearly negligible, e.g. < 10% reduction.

You don't have to share your personal situation and I'm sorry to read that you are struggling. My point isn't to argue that you must do like everyone else or that consumerism is good, rather than in the typical case (not a lot of time, hardware getting cheaper of the year, game assets being compressed already) switching to newer hardware is a much much more convenient solution. That's why I warned about it.