To solve the issue, I essentially had to shrink my nail bed back. It is ridiculously annoying, and involves pain (but hey, we're already dealing with a damn papercut right at the edge of our finger nail), and takes anywhere from 5-12 days to complete the process.

The way I saw it, if that raw/cut area kept healing back to the finger nail - I would just repeal it back away from the nail the next time I go to bend a string. So I essentially want that raw/cut area to heal over, but without having it reattach.

Here's the painful part - I essentially would lightly pull the flesh of my fingertip AWAY from the nail bed. Yes - this is essentially opening a wound; hence the pain. 

The good news is that after doing it for a bit - it becomes tolerable, and henceforth - ridiculously annoying. 

Things to manage and consider -
- You are attempting to keep an open wound from healing closed for a period of time. Eventually it will heal - most of the healing gets done overnight (so treat well especially before a nights sleep and get LOTS of sleep if you can). 
- You want to keep this area free of infection - so periodically make sure you're visually inspecting for any infection. To help prevent this from happening in the first place, wear gloves, band-aid, or tape while doing things that involve lots of exposure to diverse cultures of bacteria (e.g. washing dishes, playing with dogs, playing sports, etc.). Tea tree oil also does a good job to spot treat it throughout the day.
-USE SOME KIND OF EMOLLIENT ( any preparation or substance that has a softening or soothing effect ). You can use lotion (I don't recommend), vaseline (likely the cheapest option), chapstick, neosporin, coco butter, etc.) I found that the thicker the substance - and the longer I was able to leave it there, the longer the pain relief would last. I ended up just using the squeezable chapstick and putting just enough to cover the "paper-cut". 

-Rinse and repeat until it heals.

Once I did this I was able to do bends just fine on an electric guitar. Unfortunately, when I tried to do a full bend on an acoustic, the skin tore again. But not nearly as bad as the first time.

-Rinse and repeat all the steps again. Once I did this for a second round, the skin healed again and I can do bends without any skin tearing.

Note: In the end, I ended up making my finger pad a little bigger. This gave me a wider area to use to hit the strings. I also had to re-adjust how I hit the strings while also having to adjust my calluses. In the end it took some adjusting, but I think it feels way more natural to play.

I'm glad I went through the torture of the process - there really wasn't any way around this if I wanted to keep playing non-classical guitar. I had already dealt with this pain in the past, so intensifying it briefly and safely so that I wouldn't ever have to deal with it again was worth it in the end.

I hope this helps some of you.