in the Mixup Plus topic
we talked about "inner edges", "centre edges" or X-centres for the pieces that you call "wedges" (the pieces that do not exist on the Standard 3x3x3 Mixup.
I would prefer to stick with the terminology used in the past.
(BTW, is "wedges" not an artificial word for "wide edges", like the outer edges of a 5x5x5 edge group of three?)
In my opinion, your method is quite similar to other methods I recollect, especially the one I'm using.
If you know how to orientate a centre on a 3x3x3 Super Cube in a pure way, the early checking for a single flipped edge, when your 2x2x3 block is finished, is not a big advantage, I guess.
I flip edge FL by eight moves (E+ M' U2 M E- M' U2 M = [E+, [M':U2]] a [1,3] commutator)
The notation is old WCA plus + / - as used in the Mixup Plus thread.
M is the layer between L and R, (turn direction is noted as for L), E between U and D (turns noted as for D), - is a counter clockwise turn, + a clockwise turn of an inner layer.
This flips just a single outer edge and you need to cycle inner edges as well.
Maybe, with just the 2x2x3 solved you have a bit more freedom to do this better.
The much more tedious parity fix is the corner (or edges) swap. I can recognize this close to the solved 3x3x3 state only. Therefore, it is better to do the inner edges on the Mixup Plus at he very end (as you described it.)
DKwan had given a pure fix for the swapped corners parity, I have admired but never memorized
(The least burden for your memory is just to do a E+ or E- and resolve the cube. There are some easy to remember ways too that are not pure but less tedious to reconstruct everything.)
As a side note:
When I received the Standard Mixup last Saturday, I revisited my Mixup Plus, too.
I have to say, that after a year or so, I found it not so easy.
I looked at notes from last year about my method, but unfortunately they were not complete.
Sometimes I do not write down things that seem obvious at the time of my first solving experience. My vague memory of "How have I done this??", makes sometimes things harder at a revisit than at my first approach.