Your first probability is correct, but the ones after that are wrong because the probabilities are not independent and cannot be simply multiplied together.
There are 30 choose 6=593775 equally likely ways that 6 dim shields can be distributed into a 30 card deck.
Out of these 593775 ways, 566643 (95.43%) have at least one dim shield in the top 11 cards.
Out of these 566643, 518595 (87.34% of 593775) have at least two dim shields in the top 14 cards.
Out of these 518595, 455675 (76.74% of 593775) have at least three dim shields in the top 17 cards.
Out of these 455675, 380435 (64.07% of 593775) have at least four dim shields in the top 20 cards.
Out of these 380435, 291500 (49.09% of 593775) have at least five dim shields in the top 23 cards.
And out of these 291500, 180180 (30.34% of 593775) have all six dim shields in the top 26 cards.
However, especially in unupped play, you don't have to start chaining on the 4th turn. Yes, extra protection after the 22nd turn is useless, but the later you start a shield chain, the less likely it is that that chain will be broken by lack of shields. If you start chaining on the 7th turn (which is still before most unupped decks do 100 damage), the chance of having enough shields to reach turn 12 is 95.62% (567749/593775), and the chance of having enough shields to reach deckout is 80.49% (477939/593775).