While a reverse martingale is too simple to work, why isn't it possible to figure out some sort of betting progression in order to overcome the small house edge?

Blackjack is different from the other casino games in that the cards "have a memory" (assuming you're in a live casino where the cards aren't shuffled every hand like they are online). At various points when you're sitting down at a blackjack table it's actually a +EV game. While card counting is the most straightforward way to figure out when it's +EV, it seems like some sort of betting progression where you continued to make slightly larger bets when you were winning and slightly smaller bets while you were losing would do a good job of correctly adjusting your bet size depending on how +EV or -EV the deck was at any current time.

I'm not exactly sure which system would accomplish this, and I'm certainly not going to go to a casino and experiment anytime soon, but it just seems like some variation of a reverse d'Alembert system or a reverse labouchere system could be successful. (Not sure if I'm allowed to link to sites, but Wikipedia has explanations of both of these systems). There was some guy who "broke the bank" in Monaco using a reverse labouchere system to play roulette. People speculate that the reason the system worked was because some of the roulette wheels in Monaco at the time were unbalanced, so they favored certain numbers. Even though he didn't know which numbers were favored he was able to take advantage of this by betting on basically all the numbers for every spin, and adjusting his bets after each spin so he was betting more money on the numbers which had just come up. He won large amounts of money in just a few days and this was at roulette where there's a ~2.5 house advantage.

The roulette example doesn't translate directly to blackjack, because the roulette wheels combined with the system he had probably made the game +EV all the time. However, it seems like because blackjack swings between +EV and -EV you would be able to take advantage of the +EV times by using a similar system.