In the thought process which inspired this thread I did not so much want Italy neutral as I did neutralized. In other words, the Germans beat Italy into becoming another Hungary, Romania, or even a slightly more belligerent Spain, albeit one which has probably ceded border areas to the Reich. Thus, the Italians are not neutral, but at the same time, no real effort is made by the Germans to bail the Italians out of idiotic invasions of Egypt or Greece, the latter of which could be coopted into the Axis, perhaps bought off with southern Albania.
Sorry, but your plan would lead to even a quicker german defeat than OTL.
Italian forces in Africa were mainly infantry based, meaning that in desert warfare a highly mobile force even if smaller (like the british one, for example) could isolate and beat piecemeal the italian army. Without german support, the british would go on isolating and capturing the italians strongpoints.
Now, without Mussolini (I really can't see him staying into power with any degree of free decision in your scenario) there would have not been any invasion of Greece. This means that our ATL operation compass goes on without problems and the British kicks the fascist out of Africa in early '41. Besides they are probably able to take the Dodecanese, too. So mr Churchill now have a nice airfield (or better: a location where to build a proper airfield) which is damn near Ploesti...
At this point, I would not rule out a british attempt to invade Sicily. Successful or not, consider that from this moment on Italy is a ticking bomb. The first defeat would probably start a civil war, which would bring the front right to the german border far sooner than OTL.
The Germans would have been better off (as far as what they wanted to achieve) if forces-Italian and German, but especially the latter, had been used more uniformly in the East and not bogged down in worthless Balkan or North African pursuits.
You can achieve this by having a neutral Italy. Mussolini would probably send some volunteers against Russia, just like Franco did, and Germany could use the whole army (but the occupation troops) in the east.
Of course this frees a lot of allies troops too...