Can you provide more data, what temp does it get too?
Have you pressed the reset button on the high limit?
Is this a recent issue?
The reason I am asking is because from all that I have read from the service manual is that the burners turn off when temp is reached.
If the temp is not being reached that could be a high limit issue, a thermostat calibration issue, etc. All covered here in the service manual which is quite good. It tells you the voltage you are supposed to get, which wire gets voltage first, etc.
If you look at your burners, They have jumper ports to carry the flame from the center two that are lit by the pilot flame. Then they in-turn have two holes on the opposite side of the pilot that carry the flame to the outside burners. The outside burners have to pick up that flame to light from their transport holes. So check that the the burner side holes are clean and that the burners are in the correct position.
Standing pilot. The thermostat is set and tested at 375. Sometimes the outside 2 burners come back on when refired and sometime they don’t. The only way to get them to light again is to flip the switch on and off to the cook position.
Fix bear your theory seems to be in the ballpark of whats going on. I have taken the burners off cleaned them. Im curious as to the exact holes you’re refering too
You may need to take either a torch tip cleaner or correct size number drills to clean out the side holes. As Ectofix say’s, gas pressure is critical as well as air mixture. I don’t know how old this machine is, but they made them as far back as the eighties. If it has serious time on it you may want to do a burner and orifice tear down/cleaning. I know it’s a lot of holes to poke, but you can make it run a lot better with a few hours of patience.. It will also recover quicker and use less fuel when clean.