In the end, it was a combination of elbow grease and chemical oven cleaner that seemed to net me the best result of the multiple methods I tried.
I found that using a wire brush to score the surface of the old seasoning then applying a liberal dose of chemical cleaner overnight allowed the bare pan to be the most easily exposed.
Four cycles of re-seasoning later in the oven and I tried grilling up a batch of chocolate chip pancakes this morning. That was definitely a success.
As far as cost goes… alas between buying scouring pads, a wire brush set for my drill, and a can of oven cleaner, I probably spent close to thirty bucks to achieve what I did here. A cycle of the self-cleaning oven is not free either, but it wouldn’t have been thirty bucks.
In then end and all that said though, having tried all these alternative methods to remove the old seasoning, I think I might just go back to the self-cleaning oven method next time. Simple. Effective. And not so nearly smelly, painful, or expensive.