I was running CE184.108.40.206 and I did SUPEE-8788 v1. I then did a full upgrade to 1.9.3.
Now I'm running 1.9.3 and SUPEE-8788 v1. Do I still need to back out SUPEE-8788 v1 and do SUPEE-8788 v2?
I don't think you need to do anything when you upgraded to 220.127.116.11. Patch 8788 is included in the release.
Includes patches: SUPEE-5344, SUPEE-5994, SUPEE-6237, SUPEE-6285, SUPEE-6482, SUPEE-6788, SUPEE-7616, SUPEE-7405, SUPEE-7405 v1.1, SUPEE-8788
Any changes made to the core files are overwritten when you upgrade. You can consider your install as a fresh 18.104.22.168 with above patches applied. So you won't need to do anything regarding Patch 8788.