Should have skipped Morocco and Algeria entirely and gone directly for Sardinia and Tunisia; strike a deal with the French, maybe help them get their fleet out of Toulon and rendezvous with it somewhere in the Med. Would have shaved months off of their timetable.
But this is beside the point.
Anyway, regarding supplies - lets assume Rommel has unlimited supplies in Egypt. He can keep driving around indefinitely or whatever. The odds are still stacked overwhelmingly against him:
121 German tanks (most of them short barreled Pz3 and Pz4) and 150 crappy Italian tanks.
vs.
**at least**
300 Allied tanks (most of them Shermans).
Also, apparently, at the time of 2nd El Alemain, the British had
200 tanks available as replacements and over 1,000 tanks were in various stages of repair, overhaul or being modified within workshops.[8]
which I didn't even count. (the Germans OTOH had just 23 under repair, which I excluded). And this is with the British suffering 3-1 casualties in all previous battles. Bringing in at least half of those online for a battle sometime in mid-to-late November makes things so loopsided it's not even funny.
Lastly, to assume Alexandria will be operational anytime soon is IMO wrong - the British were many things, but they were not stupid. They would sabotage the shit out of that port, and launch air attacks with their vastly more powerful airforce to keep it that way.
you haven't allowed for the capture of other ports.
what other ports?
plus British naval strength would be minimal once that port is lost even if they evacuate to Cyprus due to the lack of supplies and repair facilities there.
They would have been kicked out of Alexandria for 1 - 1 1/2 months, hardly enough time to degrade the Mediterranean Fleet (which can also base itself at the former French bases in Syria/Lebanon, not just Cyprus)
while the threat to the Italians on the Suez is pretty minimal from the East or south given how long it would take to put together a new force from scratch once the 8th army is wiped out.
There was stuff already on its way from Britain as Alam Halfa was ongoing, which you conveniently ignore. Stuff that arrived OTL but somehow doesn't TTL. Along with various forces the British still had in the area that could be recalled, like e.g. entire divisions chasing around harmless Italian infantry units throughout East Africa.