Second favorite is my Submariner model 5513 (1978), it's nearly perfect and I still have the box and paperwork. Plastic crystal has a couple light scratches which could be polished out. At some point I'm going to attempt to have it regulated, it gains about 8 seconds an hour right now.
Nice Sub, and I love the look(what some people call patina) on the dial.
Just a quick comment on regulating...back when I first got my Datejust, which is a couple years newer than your Sub although it has a 3035 instead of a 1570.
In any case, it was okay but too far off for my liking(a couple of seconds a day). I put it on my ancient timing machine, charted it by position, and stopped by a local watchmaker to see if he could regulate it(I brought the tape with me). It's beyond me to do it myself, as I don't have a Microstella wrench and wouldn't use it often enough to make it worth getting one.
In any case, the watchmaker looked at the tape I handed him and said "You need a new timing machine." He then tossed it on his and showed me the screen. He pointed out a subtle sinusoidal pattern on the trace that was there in all positions, but most apparently dial up and dial down. Without saying too much else(he's a Russian guy and not particularly prone to drawn out conversations) he unscrews the back(using the giant press Rolex now recommends), says "I need to adjust the hairspring", makes a few tweaks with his tweezers, then adjusts the timing screws. He sticks it back on the timing machine and it's perfect. It shows a quarter of a second a day maximum variation across positions, and dead-on dial up and stem down(the two most important positions for a wristwatch). It held a couple seconds a month from then on, and when he serviced it earlier this year he kept it to the same performance.
With that said, though, at 8 seconds an hour I think you're well beyond what can be regulated out, and there's most likely something deeper going on in it. When I see that kind of variation in any watch, the first thing I'm going to do is demagnetize it without even checking to see if it's magnetized. Often that will clear up that kind of variation. If not, you're likely looking at something more sinister. An easy fix, but unlikely, would be oil on the hairspring. A slightly sneakier, and more difficult to fix, one would be a damaged balance pivot(usually but not always, a damaged pivot will show up as dramatic dial up and dial down variation, so that's something you can easily check if say you've been primarily running it dial up and base that timing on that). Even with shock protection, a bad fall or knock can still "hammer' one of the pivots into the cap jewel and mushroom it or chip it. The shock springs at the end of the day only have so much "give" to them.
A weak mainspring will tend to affect stem positions more than dial positions, and it would have to be really bad to cause that much deviation. It could also just be way overdue for service.
A watch running that fast more than likely has very low amplitude(probably low enough that you could easily see if even with an untrained eye if you had the back off) and it's most likely because something is robbing power somewhere in the train.