The 3 layers of tape help to concentrate the honing to evening up that edge, and cutting the corners off the square edge you created....
I always use the same cheap Scotch 3m electrical tape that you buy at Wally World, believe it or not somewhere on SRP is a test that one of the guys did about thickness and uniformity of different electrical tapes and the 3m was the most consistent

I wish I knew how to use computers better, I would do one of those cool graphic drawings of what I mean here.
But trust me when I say I have tried more than just this one way that I wrote about to do these types of repairs, this is the most consistent one that I have found, there are other ways to do this but I just refuse to sit there for hours and hours of honing to get so-so results....
Try the 3 layers of tape, and you need to remember that you are not honing here you are re-setting the bevel, in fact you are re-cutting almost like they do at the factory on new razors... If you watch those vids you will see they actually lift the spines on the razors...
Now I am not saying to be grinding on the razor but I am also not saying to use no pressure, at this stage a little pressure is necessary to get the edge cut evenly.... In fact I would recommend trying a two handed honing approach here, using the second hand to help keep the razor nice and even on the hone....
Let us know how it goes?????