If I provide every transaction on the blockchain from my bank account to the final exchange, except for the mixer where I can't show blockchain details, but I can show amount correlation and transaction clusters, would that be enough to get my funds released?
It's a bit unclear why you would go through the mixer at all, if before the start of the process, the bank knows about these funds of yours, and also after everything you plan to show the money to the bank again. In that case, you don't need a mixer at all.
So you're saying there is no way to use a mixer and cash that crypto out to fiat at an exchange?
Jambler has some very restrictive conditions for coins in their network. From there you usually get coins from exchanges or mining pools, see one of their partners