Seems to me you'll be spending big bucks, capriciously. As u think about it, this would make sense if u decided to raise the pitch high enough to to have a walk-in attic,etc.
The other over-riding criterion, you must just have the look you desire. Can't rationalize that.
If stopping leaks is the only real objective, tear off the old shingles (wait until you check on the disposal fees) and install new shingles. I'm presently doing a dual pitch, 2:12 and 4:12. The latter is applicable for standard shingles, I'm using GAF's asphalt TimberLine; the 2:12 slope uses the same shingles but GAF issues special install instructions to prevent rain backup, etc. You can do it or get a pro.
If the sheathing is in bad shape then remove all the sheathing and at that time consider sistering longer rafters to your present ones and get the increased slope you desire. Then shingle.
Just my opinion since I've been agonizing over a similar project for 9 months. You, at least shouldn't have to add any bearing wall reinforcement, like I did. (P.E costs.)