dead battery overnight audio system?

You've done some troubleshooting and testing but I didn't see anywhere where you said you put a new battery in.  DYohn's troubleshooting suggestion #1 will verify for you whether the audio system is causing a drainage problem or not.  My immediate thought is that the battery is shot and needs to be replaced.  Is that possible with a car as recent as 2006?  Oh yes, as every extra demand that is put on it shortens its life.  Biggest damaging factor is running it down to the point it has to be recharged.

With the new battery, you should also look into upgrading the Big 3 to help out that power supply.

Note:  Caps don't use remote turn-on wires.  They recharge immediately upon discharge.  This puts an additional strain on the battery which has to feed amperage to the cap and then get recharged itself.  LEDs pull extremely little amperage and shouldn't be a concern even if they have been staying lit.

I think we (or at least I) try to get a feel for the way someone uses his sound system by the little bit of information we read in the posts.  Two amplifiers rated at 2500 watts each is surreal.  If they, in fact, were putting out that much power you are indeed a candidate for a very high output alternator as the available capacity left over in a stock alt wouldn't nearly cover the added load of the system.  But I don't think this is the case and the system is not used that way.  What I surmise, though, is that you play it a lot and often when the car is either idling or off.  That's kinda normal.

The alternator, be it stock or aftermarket, powers at its fullest when the engine is rev'd, like as if you were always driving highway.  And daytime is better because the headlamps aren't pulling their respective load on it.  But, usually, systems are best enjoyed while parking, idling, night time, stuff like that.  The alt can't produce enough in those situations.  Instead, the battery supplies the needed amps and is constantly, but slowly, being recharged when it has a chance to.  While the alternator is likely not "too weak" to resupply the battery, it just doesn't have enough time to do it while the extra loads are turned off.

Something about batteries:  a warm battery performs better than a cold battery.  Often its the case where you can restart a car with a weak battery soon after you turn it off (while it is warm) but not after waiting for a complete cooldown.  I think this might be what you are experiencing.  Just the couple of jumpstarts you mentioned will result in a battery whose life is shortlived.

The capacitor in your system is adding to the problem at this time.  I suggest you remove it and listen for a decrease in bass response.  I am willing to bet you don't hear a change.  If it is not improving your system it is doing nothing but presenting another load on the battery.  If it is not improving it is degrading.

Something I've done in the past:  I have traded batteries from another family vehicle, without the knowledge of any other parties (!), for the sole purpose of troubleshooting.  That's the key word:  troubleshooting.  Rules and mores can be bent and nearly broken for this divine purpose.