I think at least part of the reason for the extra thickness you mention is that you have used much more overlap than necessary so a rewrap might help from that point of view. The glue strip (if present) or the gel strip in the middle should mostly be in contact with the bar rather than contacting the tape beneath.
I'm surprised you even had enough left to overlap that much on the tops!
GPWM
The reason I went with that overlap was because of the issue of starting - moving from a 90
o wrap and because I could, the impact on the thickness is obvious when you consider it for more than 0.5 nanosecond.
So, try 2. To accommodate the first turn, I started the wrap at the top rather than the bottom, then wrap a turn and a half before starting to angle. I now have two different wraps on each side. The left I used a sharper angle to start and the result possibly feels better than the right, which starts of shallower and looks more even.
One side is going to have to be re-wrapped, I suspect the left. As to how I could get away with the overlap, WYSIWYW(rap), there's remarkably little to wrap, but they are brilliant bars for a commuter with three positions - hoods, corner and flats