Alright, here is the result.
Most of it I judged by how much Harry reacted when I cut, touched, or opened a certain area. He DID have an infection in there. But a lot of it... is fleshy. I wasn't able to pull out any plugs, but I did get lots of cheesy mess. The entire bump ended up being cut in a criss-cross pattern and I squeezed all of it, long after cutting. I even removed an entire piece of skin about 1cm wide, and 2cm long.
The infection looks like it was caused by... an ingrown feather. Keep in mind that this SHOULD be the top of his toe - it shouldn't be underneath him at all. So he's always quite literally walking on feather shafts that want to grow. And it looks like one failed to break through the skin because it has his toe turned upside down so he's walking on the mass.
But even though I didn't find a plug, I did squeeze the living daylights out of it until everything came out. The only thing I got in the end was just blood.
The growth will still be there. At least for now. I got the infection mess out, and decided to stop there for tonight. It took me about 1.5 hours to "go through" the entire mass and check it all for infection. Harry actually laid on his back most of the time, only trying to flip over now and then when I hit a fleshy part. After I wasn't seeing anymore white mess, I pressed gauze up against it for a while to stop the bleeding, used a tiny syringe and needle to drip Duramycin directly onto all open areas, spread Neosporin across the entire thing and overlapped it onto his leg scales, and covered it with fresh gauze and bandaging.
I used the very last of the bandaging for that roll (previously used on a cat) so I then used the cardboard tube to go ahead and try to separate his toes and force the folded one back out. Then I bandaged the whole thing in place so the tube would stay in place "pushing" the toe outwards away from the heel of his foot.
Then, keeping him upside down, I rinsed the blood and iodine solution off of the rest of his body (he would have stayed clean if he had stayed still). Right now he's sitting in my lap wrapped in a towel. The bad foot (and the tube it's bandaged to) are propped out to the side hanging off of my leg. The good foot is underneath him. He keeps drifting off to sleep, but with the lights on here, and my typing, he won't fully close his eyes.
I'm sure he'll be okay after tonight. And I'll work on getting rid of the remainder of the growth later. Seeing dark red fleshy areas when I was cutting leads me to believe it will have to be done carefully, and possibly over time - giving his body a chance to replace and repair as I cut it away.