I will have to look at some cases similar regarding 80's construction plumbing issues. What comes to mind at the moment, I don't think I will go into that. Clearly the problem moves down the pipes, pressure of course is a major factor. Your water pressure is the same setting when the house/structure was built. Since there is no flooding the leaks form at the fittings joints,a guess but most likely a good guess. The pipes come up through the slab and there are probable 90's or whatever the plumbing scenario calls for at the bend-joints. It might be helpful to get a copy of the plumbing blue prints, obtainable for a small fee -county building permits.
Off the top,I think you need to find a plumber in your area that knows a lot about 80's construction and areas all about cutting corners.If you were to re plumb from the meter -under ground -than on up into the unit, that is a major expense. Any plumbing outfit would love to get that big ticket order. But, it is really necessary ? That is where you need a good plumbing trouble shooter to find out and tell you what needs to be done to correct the problem and what doesn't need to be done. It seems by your description the problem areas are at the joints where the pipes come up through the slab and at intersecting joints. Leaks will generally form at welds and joints that loss en over time under pressure.
You don't need roto rooter or some big plumbing outfit coming out there fooling you into thinking all your plumbing is bad and it's time for all new.
You can call a plumbing supplier, where you buy the plumbing supplies and ask for a consult. Describe the problem in that the leak moves down the pipes after a repair. Provide the same information you provided here. They will give you best case scenario and worst case. My guess is the cost of repair is far far less than what it would cost to re plumb the place.32 years is not old on those copper pipes.And don't leave out 80's construction !
And if you have to get five or six plumbing estimates before a decent plumber tell you the truth, than just keep getting estimates, those are free.
The last problem I had with plumbing was a clogged main drain-under ground. I don't dig or even run snakes anymore. A plumbing outfit gave me an estimate of $3,000 to fix it. I said screw you and take yer bi dd and shove it. I called an independent plumber described the problem -and where and what I thought the problem is. He looked at it,called me back and said yer right. Got fixed for $200. Big difference right ? Would have cost me that much just to get there.