Stuck control levers are common with generators that have been stored without fuel. If the nuts securing the IP to block look untouched with complete CARC, don't pull the IP.
Take off the governor solenoid, the starter lockout and the full throttle limit stud (count turns or measure to properly reinstall). Bend the tabs securing the two screws which hold the control lever in place. Then remove these two screws. Good luck there, space is still limited. Now with the securing plate loose, the control lever can be pulled. On the end is the pawl which converts the rotary motion of the control lever to linear movement of the control collar. You will need a small dental mirror to see the collar's position. This is critical to reassembly.
With the collar removed, clean it until it is free. Ultrasonic with Berryman B12, Pro Shot Copper Solvent IV or other good solvents (penetrating oil won't, biodiesel MIGHT).
DO NOT LOSE THE PAWL!!! Remove it and fill the hole with grease. Now slowly push the pawl back in. The grease retains the pawl, for ease of reassembly and safety. Note position of the groove on the control collar and how the tang on the pawl interfaces. You have to align the position of the pawl to reassemble. Now carefully push the control lever back into the IP. It will only seat when the pawl properly engages the slot on the collar. Trial and error, you will get it. Eventually.
If the lever is free but doesn't move easily when assembled, a blast of B12 might help. Be aware it swells the o-rings so once the collar is free, flush the pump with diesel. B12 also is poor lubricant so never operate with it in the IP.