At a minimum, I would get rid of the Amal Mark 1 concentric. This will solve most starting and loading-up problems. AJS-UK has a manifold to adapt a modern hose-mounted carb. I run the Amal Mark 2 "Square Barrel" from AJS-UK. It works about as well as anything I've used. Easy to tune and runs clean. Mikunis will fit the manifold also.
Other parts you should ditch are the original ignition stator and coil. AJS-UK has updated parts made with modern materials to give a more reliable spark. You can also get a CDI ignition system for it if you want. Myself, I like tinkering with points. The major problem with the original stator is the spade-type connections where the wiring harness plugs in. These tend to corrode over time and will cause misfire. If finances don't permit a new stator, at least solder the wiring harness direct to the stator.
Check to see if your clutch is retained on the transmission mainshaft by a snap ring (circlip). You have to pull the clutch apart. Get the special tool and service
manual for the clutch removal procedure or it will fly apart and try to kill you. If your clutch has a snap ring, pull the transmission mainshaft and have it machined for an e-clip, or buy an updated mainshaft from AJS. This will keep your clutch from falling off. If you can't replace the mainshaft right away, and the groove for the circlip is machined deep enough, you can get away with replacing the circlip with a new good quality clip once in awhile.
Keep a fresh top end in it, keep it timed properly, and accept the fact that it is a mid-range torquer and will not scream bloody murder like the Japanese bikes and it will probably run well for you. Use a good quality 2-cycle oil, made for air cooled engines, preferably a castor oil, and mix it no leaner than 32:1. The engine has a bushing on the small end of the connecting rod instead of the more familiar needle bearing, and it is not well served by leaner oil ratios.
Keep a close eye on the chain tension and condition because if the chain comes off you will probably take out the inner chaincase.
AJS-UK has other upgrades to make the Stormer easier to live with, such as serrated footpegs, better fork seals, thicker seat foam and updated brake shoes for better stopping. I have found all of these products worthwhile.
Mike