Before you start the pony motor off your clean gas supply, make sure the governor arm is free to move. It should snap the throttle wide open when you push the throttle control in. The control pulls the throttle/governor arm to slow the engine and/or limit the governor in responding to a load.
If you can't get gasoline through it, most of the worst clogs can be resolved by removing the top of the bowl which gets the float, needle and seat and high speed mix needle off and gives access to the main and compensator jets in the bottom of the bowl. There are also two plugs in the bowl, one is a drain and the other on the corner exposes the high speed metering well which is removable. A good cleaning will usually at least get it where it will run with the choke on all the time.
Initial adjustment is one turn open on the high speed mixture adjustment screw in the top of the bowl and a half turn open on the idle mixture screw over on the opposite side of the carburetor venturi from the bowl. The high speed screw is adjusted out to richen the mixture, but the idle speed screw is adjusted IN richen the mix.
Another thing to watch out for is if you remove the bowl from the side of the carburetor body, the gasket should have two rings of material, sort of a bulls eye. Sometimes the center ring is gone and it won't run very well or at all that way.
Depending on how the diesel governor throttle was left, the rack may be stuck open or closed. It might be prudent to remove the cover on the side of the injection pump and watch the rack move back and forth as you move the throttle control BEFORE you start it up. If it's stuck it's usually a pump plunger that's holding it, so spray them and work any stuck ones up and down so they loosen up and twist freely in the pump and the rack will usually free up. The injection pump housing has it's own oil supply so you can check it while you're right there.
Sounds like a good plan on the 7. That might just do it.
I would also spend some time draining any accumulated water from the bottom of all the gear cases, and fuel tanks, filter housings and crankcase(s) of the engines before you disturb things and mix the water with the fuel/lube on top. It only takes loosening the plugs and see what seeps out to find and get rid of a lot of gunk and avoid mixing it all in. If you need to bleed the fuel system after draining the filter housing etc, use a section of inner tube with a valve stem on it, clamped onto the fuel tank filler to pressurize the tank and force fuel through the system all the way to the injectors.
Magneto points should be gapped 0.014" to 0.018". Like Charlie says, after 10 years they usually have a layer of corrosion on them that must be filed off to get them to conduct. Be careful putting the cap back on the magneto, the brushes are sort of delicate and you don't want to have to stop and look up some of those before cranking it up.
D2-5J's, D6-9U's, D318 and D333 power units, 12E-99E grader, 922B & 944A wheel loaders, D330C generator set, DW20 water tanker and a bunch of Jersey cows to take care of in my spare time:D