I'm wondering if it's safe to overfill an old tank made in the 70's, and if dive shops will do it?
Well the age doesn't have anything to do with it. Whether its "safe" to overfill any tank is a different topic that has certainly been bantered around. And there are degrees of overfill....filling a 2475PSI tank to, say 2700, is a very different affair than filling a 2600 PSI tank to 3500 as has been known to happen in the Fl cave country. I've found that some dive shops will go to 2250, some to 2475, some just assume all tanks are 3000.....IOW who knows what kind of chaos is going on. On the rare occasion that I need more gas and can't get a slight overfill, I transfill the last few hundred PSI from my HP100. I think that's happened once or twice in the several years I've owned the LP72s, usually with my LP72 doubles that I'm going to use for several dives w/out a fill.
To inspect it, you need some sort of light-on-a-stick. A strand of LED christmas lights works well, or any kind of inspection light that you can insert into the tank, then just look around. If you see big rust spots, deep pits, or anything that scares you, just walk away. A covering of light surface rust can be easily tumbled or whipped. If you're near any vintage divers in SoCal, (I think the freedom plate builder ZKY is there) I'm sure they'll help you.
The "shorty" tank you saw in craigslist is something different, it's either a LP or MP modern faber. I don't know anything about them, but if they're really short and really negative you might have some of the same trim issues that the HP80 is known for.
For the valve you'll have to find a DIN valve and replace the yoke valve. The tanks you posted about all appear to be using standard size valves. Alternatively you can put a DIN/yoke spin on adapter on your tank. Those work fine and they're handy to have if you only have DIN regs, but they do put the reg closer to your back.