Don't have that specific deck, but... a couple of suggestion to check.
First of all, Program 4 = you're testing with a stereo tape.
Depending on the decks, quad 8 players can handle stereo tapes in two ways:
A) Program 1 and 3 are read with the tape head in the same position, for P1 are activated the "front" head, for P3 the "rear" head. Moving below a step, P2 and P4 are read in the same way. So... THE TAPE HEAD HAS ONLY TWO POSITION, up and down, and there is a switch on the heads to activate, in stereo mode, the front or the rear ones..
B) All 4 programs are read by the same head, as if it was a stereo head; the "rear" head is not used at all. So... THE TAPE HEAD HAS FOUR POSITION.
How does it behave your deck?
Because, if ONLY P4 has a bleeding and your situation is B, i would look for something that keep the head to get the correct position; probably below the head, or the ramp.
If your situation is A, check out if also P2 suffers from bleeding as P4; if yes, same as above.
If your situation is A and the bleeding is really only on P4... see the switch that manage the head that goes to the amplifier.