Trouble with a Lionel k-4 (6-28023)

The antenna is almost surely the handrails, as that is where it is on almost all of Lionel's diecast steamers.  You might check to see if it's become disconnected inside the shell.  Perhaps only one of the handrails is connected.

That is most likely caused by metal above the engine there. In many of the posts they suggest grounding that to earth ground to eliminate the interference with normal operation. Maybe place a metal screen or sheet under the upper tracks.

Loose handrail/antenna would not seem to cause the same problem in the same spot only.

Well, that's not necessarily true.  If it's a poor antenna, a weak signal is first place you see it.

If all of the other engines work fine, there is clearly something different about this one.

Another possibility is a weak receiver in the R2LC, that's been discussed on the forum a number of times.

John, due to the fact his other locomotives run fine, I agree with you.  The only thing I would throw in the mix before getting to the R2 would be to take his continuity meter and put one probe on ground and the other on the handrail antenna.  If no continuity, pull the R2 andr reseat it.  If he does have continuity, find where the antenna (handrail) is touching ground.  I see this often on engines that have been apart from time to time.  Also check pin 23 on the R2 to the handrails and hopefully get continuity.

Yep, my first step would be to verify the antennas are good and connected properly, not to mention not shorted to the frame.  Next, I'd have to start thinking about the receiver.  Not many things on an individual TMCC engine that will affect signal like that if it's not the layout.