I wouldn't use the word embarrassing. Despite my own clearly expressed opinions, it is a reasonable question to ask.
Don’t know if you’re just confining the question to HWs but based on listings of 66” vs 78”, there was Duran vs Hearns. An even 1 foot disadvantage with Roberto also dropping about 6” in height. Insane. Oh, and of course there was Patterson 71” vs Liston 84”. One might conclude a brutally negative correlate just based on the above two examples.
I tend to agree though I could see Conn with his fast hands and terrier-like constitution having success in a few good, spirited spells before eventually having holes punched in him sometime after the 8th round or so. The other thing with Liston is that he was technically very sharp for a heavyweight as well being physically monstrous despite not being quick. One of the very best in that regard along with Charles. Good planes of movement from the knees up, a very good punch slipper/blocker and transitioner into varied, precise attacks and such. Very well suited to tackling technical, smaller types not using excessive movement. I tend to think that Conn raised his game against Louis to a once in a lifetime type level that is hard to repeat, while Louis was undercooked and sluggish.
Conn did absorb plenty of heavy shots from Louis throughout that fight imo. Plenty. He was immensely tough and fearless, I don't think Liston would just cave him in like Patterson despite Patterson being bigger than Billy.
I think it would be 7th round stoppage. Conn is better than Whitehurst or Machen and they last long. If he survives after 7th round he would win by SD or lose by SD.