Sorry to hear about the trouble with the car which must be proving to be frustrating. Dont give up yet because Alfas are great cars to own and drive. As for the unfortunate problem that you are facing, I would take it from the many experienced Alfa owners here, many of them are as experienced and as good as any professional mechanics that you can find and some are infact professional mechanics. So I would take what they suggest to be the likely reason/s for the problem.
If having gone through the troubleshooting process and you cannot arrive at what is causing the backfire, you would want to go back to basics and start from there. That way, the chances of you succeeding in licking the problem is higher and we would have another alfa on the road
Leaving aside the issue of not getting spark, I would imagine that even when you sort out the spark issue you would probably experience the same backfire popping thing all over again and as such, it is a good thing to check timing since that is one of the basics in engine management and maintenance. I think someone has already gone through this step in great detail so I will not attempt to offer since I cannot improve on the instructions given already.
By the way, your car isn't running some kind of electronic iginition thing right?
One more thing, you dont need a timing light to set static timing. Just locate the timing marking on the pulley and set the distributor according. This is not difficult at all as I think you probably would have done something similar before. Even if not, it takes no more than 10-15 mins to set it right from scratch. You can do the dynamic timing when you get your timing light.
If you do not have an Alfa workshop manual you might want to consider getting one. It is very useful. I have only had my car for 1+ year though I have had cars for the last 15 years. Until I got my Alfa, I didnt know a thing about cars let alone work on them. Thanks to this site and the tons of accurate and helpful advise and the assistance of the workshop manual, I have since done amongst other things head gasket job, distributor timing, cam timing, radiator and alternator rebuilts, rewired my whole car and more. So I would trust and go with the advise from this board
All the best and hope you get your car back on the road soon.