Thinking of it. The microprogram counter has to be in the backplane since it gets to the KM11 board. I just don't know what pins. It has to be in the schematic. Ahh. The NXT field is in the backplane. But that is good enough.
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If I parse the the MPC value you gave above I think it ends up in 277 octal. Unfortunately it is not a valid microprogramstep. If you look at the microprogram listing in the schematic you will see that it starts of at 000 octal (the inital condition when the MPC is reset) and then progress through 241, 347, 074, 351 and then 305 which dispatches what to do next, execute instruction or handle a key or whatever.
One thing to keep in mind is that the MPC bus is an open collector bus. Several outputs can wire-or in here to modify the NXT field, creating conditional micro-jumps.
A broken PROM or OC-driver could make that you ended up in an invalid micro-step. If we have the entire flow from startup it would be easier to understand what is going on. I see one difficulty though when examining the schematic. The CLR signal to the MPC is directly from VCC. So a reset of MPC can only be caused when the system is powered up. Unless you can force it low for a short period, which could be done using a toggle switch and a debouncing-circuit and wire it to the RESET line of E101 and E111. Trigger the logic analyzer on reset going high and see what is coming on the MPC bus in the backplane clocked by the processor clock on pin 9.