Even if the start date would always have to be June 22 1941, you could possibly theoretically still edit the scenario to start "earlier" by changing everything else (weather, units), except the start date, to accomodate an earlier start, although the number of possible turns could be a problem for a full campaign. In that case, turn 1 would officially still be called June 22-June 26, but it might as well be March 1941 or any other date, if I understand the problem correctly.
The reason why the Germans had to delay Barbarossa is that they had to overrun the Balkans and Greece with divisions earmarked for Barbarossa to protect their southern flank. If you put allied forces into Yugoslavia and Greece and be ready for them to attack the Germans, then you should be allowed to move the Barbarossa date.
Why would those Allied forces be in Greece or Yugoslavia and more importantly: how would they get there? They would probably have to invade Yugoslavia, and possibly Greece as well for that to happen. Metaxas and George II might allow British troops on Greek soil, but letting them invade Bulgaria, Albania or Yugoslavia from Greek soil would be a different matter. If you would move the timetable to, say, early March, Prince Paul would still control Yugoslavia (in this alternate history scenario, the Germans could possibly see the political difficulties joining the Tripartite Pact would put Paul in, so they would not ask him to do so). Even with Peter II on the throne, it's pretty unlikely he would allow the British to just walk into Yugoslavia and launch an invasion of Axis territory from there.
Of course, all of that is mostly irrelevant from the perspective that there's no way the British would be able to launch an invasion in 1941, as they would be launching an invasion with less than 100.000 men, many of which would be inexperienced and with little to no means to keep them supplied. They would also be fighting a war on German terms and they would probably all end up dead or as POW's. The main problem the lack of an invasion of Yugoslavia and Greece would pose to the Axis would be that the campaign in North Africa would be even more doomed to fail than it was in real life. An Allied invasion of Axis soil from Yugoslavia or Greece in 1941 is not really something that could've happened in real life, whilst moving the Barbarossa timetable back 3 months isn't all that improbable.
As an aside, by now the Q&A thread needs a summary companion thread for a short summary of all the questions and answers asked thus far. I doubt most people looking for an answer to a certain question would browse through 32 pages and all the other question related threads.
