Unless your old BB is actually worn out, I wouldn't do it. With new balls and grease the old one would be just as good as the new, in my opinion.
I wouldn't call it overhang. Some BB spindles are symmetrical, others are not. If your old spindle is 32-52-35, then one end is 3 mm longer than the other, presumably to make room for the chain rings. If a 122 mm cartridge is symmetrical, then the right end should be the same length as your old one (which is what you want), while the left end is a little longer (which won't matter).
Thanks!
The bearings are loud and they make ticking noises. I haven't dealt with BBs yet but if for example a hub has the same problem you need new cones and ball bearings, a clean and re-grease won't fix it. At least in my experience.
Also the spindle is a little bit bent on the drive side. I'm pretty sure it has never been maintained or changed and the bike is from 198x.