Well... the coin example isn't really fair because the odds are always exactly 50/50, while they're different for each hand in blackjack.

However, after reading your entire post I realized that you're right and I was able to figure out where my error was. I thought that losing a hand was an indication that the remaining deck was now stacked slightly more in your favor, and I see now that that's not the case. It might be true to a very small extent but nowhere near the .5% that needs to be overcome.