No dilemma
The skilled shuffle trackers says that a shoe is truely randomed after 120-180 shuffles.
Don't know where you got that figure. The generally quoted figures are seven shuffles for a single-deck, nine for eight decks. These figures are a little misleading based on a Persi Diaconis study that was nothing to do with blackjack. Because in blackjack suits and court cards (other than being valued 10) have no purpose it is easier to randomize a deck for practical purposes.
So in this time the game should be a variation on a theme (like in music) and if in 3-4 shoes the dealer is rarely busting when his upcard is a low card that means the game will go on like this long time.
No discernable correlation exists between dealer busting and the shuffle.
It sounds like you have been got at by Patterson/Davis/Benson or other clumping guru?