F20 Farmall wont stay running

I have a 35 model F20 that I've been working on for some time now. I have it basically done except it will not run past idle. It will sit there and idle all day long but when I pull the throttle back it runs great for about 30 seconds then coughs, spits and misses out and backfires. It is putting blue flames out the exhaust. I have attached a small gas tank directly to the carburetor and it improves the problem, then when I hook it back up to the tractors tank it starts acting up again. The tank is clean and has had sealer put in it, I put a two different new sediment bulbs on it and replaced the fuel lines thinking it may be a fuel restriction. I finally ran a clear fuel line from the sediment bulb to the carburetor and can visually see good, constant fuel flow. When it dies I have opened the carburetor drain and gas comes out. It has a freshly rebuilt magneto, I checked fire and it is firing until engine quits spinning. When it is running I can adjust the load screw and it does change how the engine runs, but when I change the idle screw it makes no changes at all. I have cleaned the carburetor and put a new kit in it and the float is good. I've tried changing the timing both directions with no help, it does seem to run a little better with the mag not fully advanced. I did open the spark plug gap and thought that helped a little but it still wont run past idle and when I drive it around the yard it runs awful. The tractor isn't mine and had been setting in a garage about 20 years before I got it to work on so I don't know how it ran previously. Is there something simple I'm missing? Any advice would be appreciated.

is the timing set correctly? first on the list after the valve lash adjustment. you have given no spec's as to what you have things set at.

Blue flame out the exhaust is late ignition timing. That would also explain why it runs fine at idle but not at higher RPMs when it needs advance. First thing to confirm is that the impulse trips at TDC and that your TDC mark is correct.

Is your governor operating? Broken or missing springs?

Check your manifold I had one doing the same thing over 30 years ago. Found a hole rusted through the manifold between intake and exhaust. Look down inside your exhaust pipe my rust hole was the size of a dime. This would let fuel be sucked into to exhaust as it was running back firing and blue frames. It took me awhile to find it I too thought timing or fuel supply, But had to replace the manifold.

I suspect that you have a constant-speed governor. Many farmers upgraded to a variable-speed governor. My F-30 has the constant speed governor.
Use the steering column control (not the one connected to the mag) in conjunction with the throttle to control the engine speed.

The levers on the steering column have both been disconnected at some point in time. It has a throttle lever down the right hand side of the fuel tank that runs to the governor. The levers and rods are still on the steering column but nothing is there to hook them up.

After reading all the replies I will re check the mag timing. I have an old blue ribbon magneto manual and I timed the mag by its instructions but I will check it again, and I will re check the valve clearance. I really felt like it was a carburetor issue since I couldn't get any response from the idle adjusting screw, but I'll start rechecking everything again.

Ill look at that, it could very well be rusted through somewhere. This tractor sat in a hedge row for 20 years or so. Kind of a shame it sat this long neglected because it is a one family owned tractor. Im working on it for the grandson (now in his 70's) of the man who bought it new.