Stalls on start with oddball commonality

The old gal has had some weird quirks in her 291k miles, and I've been able to figure out the majority of them, the rest i have learned to live with. But this one takes the cake. Hoping someone can help me out on here.

Truck starts fine, runs great. Every so often over the last few months it would fire up, run for a couple seconds and die out. Turn the key again and it will just crank and crank with no start. Pop the hood, disconnect the battery for a split second, turn let and starts right up. On a very rare occasion it will crank for a second longer than normal, but the overwhelming majority of the time it is running almost instantly with the key turn.
But wait, there's more. I have taken notice over time that it will only stall after starting If I turned it off previously before turning off the lights. Headlights or parking lights does not matter. If the light south is not fully off before shutting the truck down, I will have to disconnect battery after it stalls.
Known faults.... the drivers door switch (turns on interior lights) is broken, the auto- off feature for the headlights hasn't been working for a while (turns out headlights if we turn truck off and walk away and forget to) and it will randomly lock the doors of the keys are in the ignition (running or not) and I leave the cab. Other than that, she's in good shape.
Possible add-ons that could be related... I did upgrade to LED headlights and there is an aftermarket remote start installed. However, I upgraded headlights a couple years before this issue showed its head, and the remote start hasn't worked for about a year before this issue began.
Any takers on this one? Otherwise I will add it to the quirks I have learned to live with. She's too good of a truck to let little issues talk me out of.

 

OK, I'm joining you with my old gal as well.. Assuming yours is an 07 with similar miles at 295k... I would assume some corrosion on the ground cable, or it's starting to go. I'm having a similar issue and the last time I wiggled the ground cable and it pretty much started on it's own.

All the rest of the issues, it may sound like the aftermarket alarm system has lost it's mind. I would try to remove most of the alarm system, may solve your issues. I'm on the ropes about DIY and paying someone to do this.

 

Take the LED headlights and the remote start out. Return to factory configuration by fixing the faults you mentioned above, door switch etc.

 

Yeah. I would also begin with the remote start wiring/wiring