One thing that hasn't been mentioned is with the OP's method, ie that the new joists sit on 2x4s sistered to the existing ones and sitting below the top plate, results in a big lowering of the joists. By my calculation, they would be 10.5" ( 2x12)
- 3" (top plate) lower than if they were on top of the top plate. He's using 2x12 joists. That's two feet lower, which could be excessive, if that existing wall is typical house wall height in an attached garage, etc. He wanted more height, but at some point the garage has too little height. Might also run into some building code on min height.