Usually with this type of problem I would do a service starting with checking the compression with a compression tester.
Sounds like the carby is sorted but it may have a plastic float needle that is sticking ,I would buy the metal needle with the float clip.
I've had starting problems when the 3 starter bolts come loose so every motor I work on I always check the bolts are tight and always tighten the screws that hold the intake manifold to the engine as they can come loose with age.
Just to rule out any decompressor issues I would remove it and screw an old spark plug in , a short plug will do, the same plug the engine takes.
Using the plug to block the decompressor hole will allow you to now feel the compression when starting and when the motor gets hot you should be able to tell from the starter if the compression is much less when hot than when cold.(This way you don't need a Comp tester)
If the above fixes the problem then put the decompressor back in and if the problem comes back you know the decompressor needs replacing.
I'd also take the fuel hose off the carby and turn the fuel on to check the fuel flow rate from the fuel tap as I often need to clean the fuel filter to get a better flow rate.
I usually find with the metal needles the motor requires less priming to start.
