... On roofs with low pitches, I recommend a 'rubber membrane' be used on the ENTIRE roof. This membrane is a Snow and Ice Shield, and is good for keeping water out too. On 'normal' pitched roofs, it's mostly used at the eaves. (IT's 3' in width ...) But on flatter roofs, I use it on the ENTIRE roof.
Just my thoughts - Something you can think about if you end up ripping all or part of the shingles off. Yes, use a WIDE drip-edge. My best to ya and hope this helps.