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.