Progress! I have solved the 4x4x4 with only my 3x3 knowledge and algorithms.
Side note since this was called into question. I only saw that Zemdegs interview after I got stuck at the last flipped edges, so I'd already figured out how to do the edge pairing. Maybe I'd already somehow seen people solving big cubes with the centers first (wouldn't surprise me), but I don't think that's very hard to arrive at independently. It's an obvious and fairly straightforward thing to start with.
Anyway, so did I get lucky with parity? Maybe. On the first attempt I got one edge pair oriented wrong. So I unsolved a few edge pairs and tried to swap something and then I ended up with two edge pairs oriented properly but permuted wrong (blue green swapped). Then I tried again and thought I had it, but ended up with green and orange permuted wrong, and head banged the table. And then I tried again and messed up too many edge pairs and ended up with a solved cube. So do I know how to fix parity cases? Not really yet. But I did solve it without scrambling the whole thing and starting from scratch. I will keep at it until I can consistently get solved cubes even if it's not very elegant or quick.
And just to reiterate that I don't really care about how "pure" my unspoiled puzzle solving is and I'm not looking for adulation. It's just an interesting puzzle and I'm trying to figure things out the best I can.
Something which might be of interest is that in my early attempts, after solving the centers, I tried to solve layer by layer using beginner style middle layer algorithms, but it kept messing up the centers and I couldn't figure out when to do wide turns or split the middles to get the 2nd and 3rd layer edges in place. That's when I realized I had to pair ALL the edges before even starting the first layer corners.
My fumbling is probably amusing to those that really know how to solve bigger cubes, but I still don't want further hints or "yes, that's the right way to do it" yet. Just enjoy some more popcorn and we'll see where things go next.
More progress. I got a PLL parity situation, and I successfully turned it into a different PLL parity, then yet a different one, and then back to the second one. So I'm clearly changing it, but I don't know how to know if I'm changing it into something correct. Also, each time I have to resolve most of the 3x3 cube from an xcross or xxcross state, so not an efficient algorithm either.
Edit: (hey, I figured out the edit button). Turns out I'm not as clever as I thought and my different PLL situations are just the same 3x3 state with a u perm or z perm or something. Agh. Try again.