Okay, so
A) You have a voltage issue/power issue not a "starting problem." These two issues are usually confused because what you want isn't happening. The fact that it starts every time you give it enough juice would lead me to look else where.
B) Car batteries have some quirks about them. There is surface voltage and there is actual voltage. With the engine running it is expected that you will see a spike over 12 that could be +1 to +4 volts higher. This usually won't stay constant, but if I remember right there is a spec'd range of surface voltage (my word I learned working on boat engines after having to go over and over and over this with customers). Getting excited about volts isn't going to fix your problem, lets talk about AMPS and is your battery rated to the type of AMPS needed to crank this bad boy over? How old is your battery and what type of battery is it?
C) How long have you owned the vehicle without similar issues. Has it ever had problems starting, be detailed as you can be. Even if you can only say that it has happened off an on for 10 years but now just suddenly it happens every 3 days. It is pointless to discuss in any detail with just the problem for information. We need some more history about recent items you may have installed or "fixed" recently.
The first break through you have given us is that there is a bleed and that you recently did some stereo work. Telling us about the speaker install is pretty important. I have had to backward troubleshoot toooooooo many customers that have recentley installed something and forgot to mention it when dropping off a dead boat. Radios were very high on that list of things which could kill a battery.
Here is an idea - remove the fuse for the radio and leave it out for a week after ensuring the battery is good and charged. If the problem went away and does not come back you might be onto something if you know the pattern to which this issue usually shows it's head.
I have not heard of a starter bleeding down a battery unless it has had loose connection, check the connections and ensure they are tightened to spec. Alternators can sometimes bleed down a battery because they have rectifiers that create DC out of AC current. A diode internal to the alternator could failed and allow current to go backwards thus draining the battery. You need to use an amp draw meter for both scenarios to be verified. Please don't throw parts at it without testing anything. That way you can verify how much current is coming out of the battery to the culprit component.
In my experience starters and alternators are rare. It is usually a raw positive wire pinched somewhere that has current at all times. Very few items have current after the key is turned off, start looking there after you verify that there is a bleed.
Something else to pay attention too is the grounds. This little detail is very important because it is the flow of energy through your engine. Typically in Japanese made products the grounds are toggled in order to create the circuit. Be sure they are all shiny and tight. While it might not fix your issue, it is just good PM. Ensure that your ground wires are tight, clean, and protected with anti-rust/corrosion products.
Just my two cents...
While I might be crazy as hell...I have the scars to show I've learned some lessons.
