Could it be that after the strip completely clears the front feather board that the support needed, to keep a long strip straight, is gone and the pulling (or pushing) action causes the now unsupported strip to turn in, thus causing the extra 1/8 dept of cut? Despite all the support and featherboards, when the end clears the feather board it will try to turn in.

The bit used to cut a bead will pull the strip in (if not properly supported) by the way it cuts. I have used routers and shapers for years and have seen this on a few types of bits. Generally a coved type bit that cuts a bead type shape. Make sure that both sides of the strip are supported for more than 12" on the outfeed side of your router. This may end you problem.

Hope this helps.