I don't think that "winter" is a realistic proposition, there's nowhere to play in that time. But I can't seen any harm in running the entire Shield competition (including the final) between October and early January. Then going into the separate T20 competition.
the biggest issue with the domestic scheduling is
a) playing domestic matches during the time period of Test matches
b) playing T20 matches when best suited to maximise ticket sales/Revenue.
Sadly, the best time for both of these is dec 20 - jan 10 where people have time off work, and test matches are played in Melbourne and Sydney.
I don't think bringing the SS forward is the way to go. realistically, the BBL could be run much tighter - at the moment, they havent played a match since Thursday, and the final wont happen until the end of the Adelaide test. theres a good 2 weeks where they could be playing at least 10 more games without moving any FC games!
the current system, whilst not Ideal for Test cricket, works pretty well. FC and List A games take a month/6 weeks off over christmas/newyears to play T20D stuff then get back into the business end of the competition for the last 6 weeks. trying to have all of that finished by November leaves a big gap at the other end of the season.