It look like a clock problem, and testing with another 6808 was a good idea. But, does the Phi2 signal (on pin 37 / 6808) stable ? did you check it using a scope ?
I sometimes encounter strange clock behaviour (like a divide by 3 using a 7474 on 6502 systems ! ) and checking the clock at Phi2 is a base for repairing.
May be, a good idea will be to replace the XTAL (CR1, 3.579 Mhz) and the two associated capacitors (C25 and C26, 27pF). A defective capacitor may lead to an unstable clock signal.