Following your description of the coil conversion, plus the photo you posted earlier, I think it unlikely that this is the cause of the problem. You are consistent in saying that you have a spark. If we exclude jets of the wrong size, or jets fitted in the wrong places (it can be done by mixing them up) then a quick blast from the air compressor through the various passages in the carb should solve any issues there. If your petrol tank has previously been lined with a sealant this could be dissolving in modern fuel which includes ethanol but I would expect you to find some detritus or residue in the carb.
That leads me to fuel supply issues. If you fit the carb without the float chamber and turn on the petrol, do you get a good flow (into the cup you have handy to catch the petrol). Is the petrol clean in the cup or is there detritus / residue?
As a totally different possible cause of problems, take the rocker box cover off and try starting the engine. My 4G ran well for a while after I rebuilt it then started misfiring. Eventually, I found that repeated skimming of the head and rocker box had led to the point where the valves were being held open by the tappets catching on the underside of the rocker box cover. It took some time for the gaskets to bed down enough to make this happen but the bike is now fitted with 2 very thick rocker cover gaskets which has overcome the problem. You will find witness marks on the underside of the rocker box cover if this is happening on your bike. Perhaps unlikely, but very easy to check and eliminate.
Keep us posted, but after some fantastic days on the North Yorkshire Moors Railway I have appointments with one or two other steam engines over the next few days so replies will be erratic.
The photo below is from last year at the NYMR but is the only one suitable to show you on this computer at present.
36 4G, 37 VH, 54 KH(A), 75 Healey 1000/4, 52/53 ex ISDT KHA (project).
Former Machine Registrar & Archivist, General Secretary and Single Spares Organiser (over a 25 year period).
Now Archivist once more - but not Machine Registrar.