Very Nice John. Excellent write up. Your traces are really clean and unambiguous. Well done! To add more benchmarks, similar testing here pegged the delay through my IC-7610 at 4.0 mS (same as yours) and the R8600 at 12.0 mS in AM mode. Additionally, the delay through the R8600 was mode dependent.
TWO FULL SECONDS THROUGH THE KIWI!!!!!! Holy lethargy Batman! What do they do - send it to Japan for processing? The trick of summing a little of the 1 pps pulse directly into the RF input may be a viable option here. Then the timing reference and signal you are copying at least go through the receiver delay together. Just edge differentiating the leading edge through a small capacitor worked well here at 2.5 and 5 MHz but not so well at 15 MHz. But using the 1 pps pulse to trigger an on-frequency RF burst out of the function generator to get a wider pulse worked great. A 350 uS pulse width made a hump about as wide as a half cycle of the WWV timing tick and was very recognizable. It made TOF measurements easy just using a .wav file recorder.