Sounds like you have a good plan. getting rid of the flat roof all togeather would be the best thing to do. When the addition was first built instead of putting a flat or near flat roof would have been better to re-structure the roof then. But even a 12/3 is almost flat so wouldn't have made to much of a differance. Most additions that I have seen have this problem, they put a almost flat roof on the addition and left the existing roof as is. This creates a possible place for leaks to develop, and weak spots that I have been afraid to walk on. If the addition is done correctly you should not be able to tell that it's an addition, it should look as if it was always just part of the house. It is absolutely feasible, I'd suggest a hip roof (stronger, and better uplift resistance).
A word of caution though: do not create two attic spaces!! You did say 'remove the old roof' do not let a contractor try to talk you out of this!! be sure they understand that you want the old roof completely removed including the rafters.
2nd thing to make sure of is do not let the contractor brace the new roof off any ceiling joists!!! all braces should be ontop of interior walls!! I ran into this problem before and had to build a support beam above the ceiling joists ontop of the walls on one side of a house to rebrace the roof properly and make sure it didn't mess up the ceiling again. It was done by a roofer who wanted to stop the roof from sagging.
It will cost quit a bit, but short cuts on the roof, and roof structure is one thing you should not do. If you can't get it done the right way, start saving till you can. Since I'm not in your area I'm not going to try to even guesstimate the total costs.