Again, you're worrying about the wrong thing. You can ignore the small difference between these.
FWIW the 5000X schematic does have the 6013 board, just not the schematic in the commonly available service manual. NOT everything in the service manuals matches what's in the case. I've had 5000A units where individual components not only didn't match the manual but different units had a couple of different boards. Running changes often did not make it to the manuals. Originally the 5000X came out with the F-1040-1 boards.
The 6013 boards connect to the output transistors, fuses, coupling caps and the High/Low filter board. If the output transistors, coupling caps, voltages, and signal(from the filter board) are good the problem is in the 6013 boards. If you can't justify getting a cheap scope then find someone who has one to check the signal coming off the filter board. The cheap scopes might not be all that great but should be able to at least be used to trace a sine wave through the system. The only other way I can think of to check would be pull the signal wires off the filter board and connect another amp to the filter board. (not recommended)
Yes, the headphone jack is run off the amp boards.