I need to raise my garage by 16″

In my experience it is always easier to lift a complete structure rather than a stick-framed roof. By doing it the way you propose, it would be pretty much impossible to seat the rafters on the wall properly (due to the 16” change messing up the geometry), not to mention the difficulty in dealing with the sheeting, etc.

I see two options, but neither are easy… and not necessarily DIY-friendly (calling in a pro may be a good idea):

1. You can cross-brace the structure’s inside walls to ensure it is rigid in all directions, lift the entire structure, and build your 16” walls underneath. (I would use two rows of block on the slab.)

Or

2. Tear off the roof altogether and re-frame it once you have your walls done. It may seem more difficult than what you proposed, but in the end, this approach will be far easier and faster.