I think the "easiest" (and cheapest) solution is to use an external SSD. Do you all think this would improve things?
Yes, a clean install onto an NVMe drive in an TB3 (or better) enclosure will improve things dramatically. I would then not use the internal drive pair at all (either leaving it unmounted, all free space, etc). It's dying and not going to get better.
Also, I would defer the Mail and similar issues until after that is done. I would check that they haven't come back as above but it's not worth debuggiing in the current state. For example, it's possible Mail's database has been corrupted given the dying drive but I wouldn't try to do a rebuild on the current drive. Siimilarly, no need to look at uninstalling extra/unneeded software on the system. Just don't reinstall it after the clean install of the OS. Once on the clean install of the OS onto an external SSD, data restored, etc, come back here for any issues that persist.