How could they have anticipated Italian fiasco? Italians had triple the number of troops, their equipment is roughly comparable to British standard, aside from Matilda tank. Furthermore, Mussolini was this type of guy who would lash out on his own and come running back if he gets whipped.
Full panzer corps is a formidable formation, though in 1940, Germans still used Panzergruppe, an ad hoc collection of mobile units grouped together under single commander, but for the sake of argument, let's say it consists of two panzer and a motorized division. I don't have the data how much supplies they would need handy. IIRC it was around 300 tons of supplies per day for a panzer division and say 200 for a motorized one. So this unit (which is remarkably similar to later DAK) would consume around 800 to 900 tons of supply a day, or up to 30.000 tons a month. That is one third of total port capacity of North African ports available to Axis at the moment. Supplies could certainly be improvised.
We come to the tricky part now - redesign of panzers. IIRC, Panzer IV and III required extensive redesign and in case of Panzer IV they basically ended up with virtually completely new vehicle, as turret needed to be made completely anew to provide place for larger gun. This program took a year to complete. Even if they decided to do it in, say June 1940, first tanks would not be around until Barbarossa.
In 1940, Germans felt they could get along with current variant for the time being. They had some prototypes made and running, but it was a low priority programme. Only by the end of 1941 they realised T-34 was a generation ahead of their panzers and started a crash program to make a new tank. This program also brought first results by the end of 1942. After being given a high priority from Hitler himself. Even then, tanks were rushed into combat, without adequate toothing.
German PzKpFw IIIs and IVs were certainly adequate to handle British tanks in the desert up until 1942, when Grants and Shermans started appearing. Their undoing was solely logistics. I do not see how this helps.
I'll summarize my post, since I may have made a jumble out of it while writing.
1. No one could anticipate Italians would fold. They had all advantages, yet failed. It follows Germans won't be ready to bolster them any earlier than they historically did.
2. Making a decision to upgrade German changes nothing by the time of Sonnenblummen in the best case for Germans. Upgrades will be too late for effective use in February/March 1941. Germans just might have first tanks some time in October or November 1941.
3. Logistics remain the same. Heavier tanks might exasperate the problem further.