Right. So because you have separate L/R volume controls, is why these are not stereo pots. Finding one with the 4th pin is going to be nearly impossible because that 4th pin is for loudness control, and modern audio doesn't rely on separate loudness compensation circuitry anymore, typically accomplishing this with digital manipulation or dedicated audio chips. Cheaper and easier to do this way. But I digress. In any event, because current demand for slide pots with loudness compensation is very low, therefore manufacturers have for the most part, abandoned them.
However, as you are already prepared to trash the current pot and replace it, drill a hole into the boombox even, why not just rebuild the pot and see? The danger is that after fixing, that you will have slight uneven behaviour between the left and right pots due to potential alteration of the resistance taper introduced by the repair, but it should work.
Since you say that the traces appear worn and have no continuity then the solution is to apply some trace repair compound. You can get them with small nail-polish type bottles with brushes. The silver ones are probably full conductive and the black ones are probably carbon that will vary resistance based on application thickness. For you, since the silver part is what is worn, then just apply the silver stuff ONLY until it contact the still conductive black portion. Now, this repair probably won't be as durable as the original factory coating so don't fool yourself and think you'll get as much life. Furthermore, it's probably prudent to add a little oil-like preservative (such as Deoxit gold D100) so it will wear better. Just a smidgen. Also, presumably at this point, as a collector, you also have a ton of other boomboxes available to you. So I don't expect that the repaired pot will receive nearly the type of use that a new unit 35 years ago would receive since, you probably like to rotate your boxes, and probably listen to a single volume range 99% of the time anyhow.
So as there's nothing else to lose, just get and apply some (sparingly or you'll ruin the control) conductive paint or epoxy and put it back together. I mean, realistically, finding a PH470 is hard enough. Finding a slider, in good condition, for the PH470 is.... well you get the idea.
