well obviously u can crank ur idle screw up a little bit to avoid a shut down until u figure it out. i had the same problem recently but when i had my injectors cleaned and changed my spark plugs the problems went away, check ur vacume lines coming to the intake manifold, its a possibility one of them has blown off, but more likely if its drawing alot of power ur battery may not have enough amps to crank out the power necessary may need to get a higher rated one, but sounds like u've already tried most of the things that i would start with, in rare occasions it can be a fuel problem with rust in ur gas tank, something wrong with a fuel line, possibly check ur fuel filter, check ur spark plugs for any indication of engine problems, ie overheating plugs, bridged gaps etc. but good luck buddy, you sound pretty educated on what needs to be done, hope u find ur problem