There is no reason why you cant get a 2F carb running the way it should. The tragedy is, that the 'ustaads' here have a strong tendency to tear down the carb whenever the engine hesitates/missfires/runs rich/lean. There is no rocket science to tuning a carb especially when it is as simple as the ones you get on these F series motors. Before setting the carb/timing you should make sure that your cylinder compression numbers are within spec. Any bad valves/compression rings will easily show on a leak down or a simpler compression test.
What worked well for me was, setting the RPM to around 400 with the idle screw which will be at the back of the carb. Shut the engine off, turn the idle mixture control screw in till it is 'seated' and then unwind 2 turns out. This screw will be located opposite the valve cover. Turn the Idle mixture screw in quarter turn increments/decrements and stop where you get the maximum engine speed. Now all you have to do is set the engine speed to manufacturer spec, which I recall is around 650 RPM. Another thing you need to take into account is the fuel bowl level, which should be about halfway up the visor window at the front of the carb. If it is on the higher side, your mixture screw give the best idle turned slightly in(1/2-3/4 turns) and if it is a bit lower than half you will accordingly need to turn the screw out a little. Make sure you have the propoer carb kit when you rebuild yours to ensure correct jet sizes.
Moving on to the distributor, as noms56 has pointed out, there is no reason why a dizzy wont hold the timing if the rest of the timing gear is all okay. A dizzy which seemingly set right, still leaves the timing mark bouncing around is indicative of bad distributor shaft bushings, a bad timing gear, distributor gear or distributor cam. If these things are in good nick, there is no reason why your point will not hold the timing you set.
Lastly and most importantly, from my experience whith these motors, they never seem to be in that right 'tune' primarliy because of vacum leaks. This is something that our 'ustads' never seem to bother with. The age on these motors leaves the vacum hoses/pipes brittle and cracked. This is how you get 'unmetered' air into your intake and the engine runs rough no matter how hard you try to tune it. Common trouble spots for this issue are the PCV valve hose/grommet which you will find on the back end of your valve cover going into your intake manifold just beneath the carb. Another all too frequent cuplrit is the pair of bushings on your primary throttle valve linkage. They wear out with use and leave space for unmetered air entering the system. Remember, any air entering your intake manifold from beneath the carb (unmetered) is a trouble maker, air should only enter at the mouth of the carb. With these leaks sorted out, there is absolutely no reason why these carbs cant work like they should. If i might add, the 2F/3F engine will let you balance a coin on its side on the oil filler cap if you take all these things into account when you tune it. These are very well balanced/smooth running engines. Sceptics can ask me for a video of this act any time.
So to sum it up, you should:
1- Start frist of all with inspecting your sylinder condition.
2- Move to sorting out vacum leaks.
3- Set the ignition timing after checking all the components as mentioned earlier.
4- Finally you play with the carb, which i will say again, is very easy to tune.
Another thing which i believe is good practise, is to take the vehicle for a 25-30km road test after the tuning. The bes indicator of your mixture settings is the spark plug. After driving it for the said distance, pull over and open your #1 plug. It should look like its covered with rust around the electrode and tip if the mixture is right. If its towards the darker side, wind in the mixture screw a quarter turn at a time till you get that rusty colour. If its too 'white' or scaly, open the mixture screw up a little till you get that beautiful rusty colour. Such tuning gives the best results in my opinion.