I came up with a similar betting scheme a few months ago just out of curiosity. I played a few thousand hands on the basic strategy trainer, 6 decks, h17, DOA. I would bet 1 unit until I won twice in a row. Then I would bet 2 units, then 3, then 4, etc....until I pushed, lost at least one of two split hands, or lost. I would go down to about 800 then surge back to even or a little positive and slowly lose.
The first time I simmed it at home using chips and one deck just for fun, I quadrupled my money super fast.
However, keep in mind that the advantage from a positive shoe only exists from doubling, splitting, and blackjacks paying 3:2. You still win about 43% of your hands, just the hands you do win have a much higher percentage of successful doubling splitting and blackjacks (not to mention insurance I suppose).
Basically, for the non AP, that is the best progression system. A bunch of little losses offset by the occasional gigantic win. Martingale is a bunch of little wins offset by the occasional gigantic loss.
Would you rather win a tiny bit often, then lose a ton on a bad streak, or lose the minimum on a bad streak and be betting huge during an amazing streak?
You won't win long run, but it would be hard to tell through the joy of your large wins.