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This is almost exactly how I do it just a lot smoother and with some better choices. Nice. Making centers I do the stab a completed line into the center, rotate and pull the chaff out thing.
One thing you don't have to do. You can put the 4th white tredge together splitting the centers and then not have to fix the centers. Throw the white tredge on top/yellow white side up. Twist the face for the missing tredge 180, and move the white tredge in place and rotate back 180. The centers are fixable but there is no need to do it. Go do the edge pairing for the next 4 tredges split centers then fix the centers. You get to put 5 tredges together with the split centers technique.
I'm sure you can also figure out a smoother/more move efficient ways to slide in the 4th tredge but leave the centers fixable. The 180/180 is a nice demonstration of the idea of leaving the split up centers solvable.