10 Minutes of Fun...then STALLS! -Part 1 (Chrysler Crossfire)

Haven't worked on one of these little roadsters...a 2005 Chrysler Crossfire Convertible!
It's at a local shop who tells me the car just randomly STALLS out after a few minutes of driving, and WILL NOT RESTART until it cools all the way down.
Also there seems to be a PARASITIC DRAIN since the battery is always dead after it sits for a week.
Let's jump in, get it started, and collect some data. Should be a fun one :)
IVAN'S PICOSCOPE WAVEFORMS:
drive.google.c...
THINKTOOL PROS:
www.amazon.com...
Enjoy
Ivan