Just a thought - your bad alt and batt may be the culprits. You will be using a fair bit of battery in an EOC in the "run" position. Your brake lights are on, your radio may be on, your dash lights, the ECU.... if you have an alternator that is dieing, it may be innefficient at recharging and really load up your engine.
I had to replace my battery a little while back because after a long EOC, then parking the car, i couldn't restart it! i had to bump-start about 6 times in 2 weeks and the girlfriend got sick of pushing so i had to get a new batt
