Hi, Bill:
I can't figure out why Marlins shoot as well as they do, with all that stuff hanging on the barrel. My old .35 Remington has a barrel that Galliard, Hart, Lilja, Shilen et al. would trash. It has swarf rings all the way down the bore, but 90% of my 5 shot 100 yard groups stay under an inch and a half.
OK, here's a bunch of wild guesses. Obviously, the heat's moving something, but what?

I'd try loosening the fore end cap and trying that first. If the wood is sticking at both ends, then slips when the barrel expands and sticks again; that would explain why your third shot stays out after 10 minutes cooling. You'd have to let the barrel cool completely before the wood slips back again.
If the barrel hasn't been stress relieved, it may be warping as it heats up. Elmer Keith claimed a straightened barrel was pure poison because it would walk it's shots as it warmed up. How should I put this? Suppose one side of the barrel is under more tension than the other, due to straightening. You fire two shots, and the tensioned side stretches more, but not enough to change the point of impact. Now, the bore surface is hot, but the outside of the barrel is still relatively cool. Now if I'm on the right track, here's the tricky part. Metal on the inside of the bore doesn't have as much leverage as the metal on the outside of the barrel. The heat has enough time to migrate to the outside of the barrel and warp the barrel by the time you fire the third shot. Does that make sense???
Your barrel might be a candidate for the cyro treatment.
Bye
Jack