That's excellent news...well...in terms of locating the problem. Actually getting the parts to repair it might be another story.
I wasn't sure what the SOS feature was, but now looking at the schematic, it makes more sense. P4 is the SOS head. P1 - 3 are the echo playback heads. Take a look at page 13 of the reader (7-1 overall circuit diagram). You can see VR14(p4), 15(p1), 16(p2), 17(p3). These are the internal trimmers that adjust the volume of each playback head. The signal from p4 goes straight to the output jacks (after going through another buffer and mixing with the dry,chorus, and reverb signals.
The signal from p1, 2, and 3 mix together at IC13a. Before the output from the buffer at IC13a mixes back in with the p4, dry, chorus, and reverb signals, it also goes to two pots: VR6(echo intensity) and VR7(echo). I've always hated Rolands names for delay parameters. Intesity is "repeats", and echo is "delay level". I would think most people would assume that "intensity" would be the level, and "echo" would be the repeats. Anyhow...
VR6 is the feedback loop which sends signal back to the recording head. VR7 is just a passive volume knob for the echo signal. Lug 3 of both the pots are connected at the same place. The IC13a buffer is putting out signal if you are getting a constant crackle sound. The problem is that IC13a isn't getting any signal from P1, P2, or P3. This doesn't necessarily mean that the problem is with any of those playback heads. Hopefully, that isn't the problem.
So the good news is, we've narrowed down the search to a very specific part of an otherwise overwhelming circuit. If you have an oscilloscope or an audio probe, you can trace out the signal from the 3 playback heads(page12) to IC13a(page13). Hopefully, you're getting some sort of echo in there somewhere, and more importantly, you can find where it's dying. Unfortunately, there's a little bit of the schematic that got cut off between the playback heads and Q23 - 25. These are JFETs. You should be able to hear signal with an audio probe at the gate of each of these. If you can't detect any signal at the gates of those 3 JFETs, then it probably means the playback heads aren't working. It's odd that all 3 would go tits up at the same time though. Maybe they all share a common ground wire that's come loose.