On a tandem switch, "the tab" is for the usual situation where you have a black always-hot wire feeding both switches. Leave the tab and you can just hook one wire and be done.
With the tab broken off, the two switches are completely independent, and wire exactly like two normal switches.
However, these are both "old school switch loops that don't have neutral". The black and white wire are "always-hot" and "switched-hot".
By Code, the white should be always-hot (to make it more obvious that it's not neutral) and more recent Code requires it be marked with black electrical tape to flag it as not a neutral. That is because black-white is how cables come.
The rule with neutral is "You can only take neutral from cables that already have hot wires running to the switch". In your case, all 3 of the cables are totally isolated from each other - they do not share anything. So you cannot cross any wires between them. (except safety ground, which is always connected between all wires, all devices and a metal box).
This means you're out of luck with these switches.
I have no idea what the third cable is, and that might bear investigating. I gather it's not connected to neutral, or else your experiments would have "worked" (unsafely/illegally) and you would have never asked your question here. My guess is "it's a third switch loop" to a switched receptacle or light currently not working. Classically someone replaces receptacles, does not pay attention to those tabs, and effectively shorts out the switched receptacle function, making it always-hot and the switch inoperative. Sound familiar?
Anyway, if you can figure out where that third cable goes and re-task it to be "power supply hot/neutral", then you can convert this box into the normal "power into the switch box; lamps at end of runs" arrangement. You will need to cap off/isolate the hot-neutral that no longer feeds the lamps.
That would leave you without a switched receptacle: "Boo Hoo" :) If you have a working light built into the ceiling that is operated from the switch, Code is satisfied and get rid of switched receptacles.
Lastly, stop experimenting. The problem is your "win condition": you will stop experimenting the moment you hit a combination that works, right? Well, there are many combinations that will "work", and then kill you. You have the good sense not to attach neutral to ground... that helps a lot.