7.3 Engine stops at low mph during braking.

Engine - 2001 7.3 PSD, 101,000m, w/ 4" turbo back exhaust, AFE intake, using Superchips programmer at the time.

Problem: About 3 months ago, my 2001 PSD engine was stopping during low mph braking (20mph or less). The engine easily restarted after shifted to park. This was occurring initially while I was towing a 6000 lb. trailer. (During a regular weekend trip it might occur 1 time each trip). It was so rare I figured it was water in fuel. Then it began occurring while not towing, until finally stopping and not restarting. I had is towed to Ford and the Exhaust gas backpressure sensor was reported as the issue.
No problems for a few months until last week while towing a new 5th wheel it happened again with the same initial conditions. This time while stopped at the curb, I connected the SC Tuner and removed the programming taking the engine back to stock conditions. Restarted and had no more issues on the drive back.
I realize that the SC tuner may be one if the issues, but does anyone have other ideas what may also be an issue?
Maybe ULSD? The Tuner and towing was fine before ULSD was at the pumps.
Thanks for any ideas and help.

torque convertor lockup ? what coes are present?

Code P0603

P0603 - Powertrain Control Module KAM Test Error, is the only code which comes up.

I had the same issues before. I thought that the porblem may have been because of my programer, but I was wrong. I had the same code pope up. I put in a new CPS and that did the trick for me. Try the IMPOVED blue CPS. I wish that I would have done it sooner. My truck seems to run smoother all around.

By "improved Blue CPS" are you refering to the new one that FORD has out now, or the unit that is for the International 466?

Replaced the CPS yesterday, all works OK at this point, the new part did seem to even the idle. I will report back as I break in the new part, hopefully with only good news.
Thank you for the information and direction.