What's wrong with my charging system?

I have a 1983 Honda CB550SC. A month or two ago I replaced the regulator/rectifier, and yesterday I replaced the stator. The output off the stator is ~12v AC at idle, and goes up to 15 at higher RPMs.

My battery is a lithium one by Deltran. I charged it over night on Monday (13.5v), and yesterday after replacing the alternator, went for a short ride to an appointment and back home, then was going to a friends house I got a mile away from home and it just shut down. I've learned to ride with a multimeter and it was down to 9.x v. I had someone jump me and left the thing at a friends place. So with my alternator obviously putting out a charge, what is wrong here? I'm at a total loss.

Another bit of info, not sure if it's relevant or not, is that my signals speed up with higher RPMs and slow down at idle.

Sounds like your Stator is shot - new or not - check out this article
http://www.ehow.com/...tator.html
and this thread
http://www.fireblades.org/forums/honda-fireblade/65137-stator-output-voltage.html

Maybe not going to be much help here but I sorta remember an electrical part between the rectifier and the battery on a 86 CB 650, seems that part heats up and stops working for a while but also doesn't allow the charge to go to the battery. Half-way remember that I by-pssed that part but that was like 20+ yrs. Ago.
Hope that helped a little bit.

Your alternator output is way too low.
Consider that diode voltage drop is about 0.5V - 1.5V, and you can see that you don't get even 12V at idle (after the rectifier).
Blinkers changing speed and lights going dim/bright with rpm is usually a sign of regulator failure. However, if a properly performing regulator is not fed enough input voltage, it can't output the proper voltage and the same symptom will result.

Unplug the wire to the stator.
Start the engine and check for voltage output at the connector.
At high RPMs, the voltage should read between 50 - 100 AC volts.
Check at each pair of yellow wires (3 tests)
The rectifier changes the voltage to DC volts.
The regulator sends the necessary voltage to charge the battery and sends the excess to ground.

When checking voltage at the battery, your meter should be set to DC volts.
When batteries age, they lose the strength to take and hold a charge.
A poor battery can wreak havoc on electrical systems.
The regulator will be in a constant state of flux operating the bike's electrics and trying to maintain an unwilling battery.

Give the battery a good charge and have it "load tested" to check it's condition.