Uhoh.... I've been called out!!
I have the Killshot on my Cobra II as well, but haven't driven it more than probably 20 miles since. I've had to do a lot of supporting mods to get it to a point where it should be reliable. But, reading the problems you're having, I'm curious about your battery and charging system. From what I recall, these aftermarket fuel injection systems are sensitive to voltage input. It could be a combination of a few different things that have already been mentioned. So you'll want to be sure that that's all up to snuff.
What I did was a 3G alternator swap, installed a power lug that runs straight from the battery to tap into for a few different accessories that includes the Aces system, and ensured that all of my cables and associated connections were in good shape. And if your starter is heat soaked, as was mentioned, it's going to require more amperage which could potentially cause issues with the system as well.
Now, if all of that is up to snuff - which you said it all should be - it may be a fuel issue for some reason. What pressure are you running? I've got mine set to 50 pounds. I don't remember off the top of my head what they suggested for fuel per hour, but I've got an Aeromotive 18638 Stealth 340 Fuel Pump plumbed to 3/8" lines with a 5/16" return.
As far as an RFI issue, Aces recommended using their coil to eliminate that as a possibility. I was having issues with it after the intial install which turned out to be my own error, but I did go ahead and swap out my MSD Blaster for an MSD 6EFI 86415 Ignition Coil which looks exactly like the Aces unit for a bit cheaper. So if that's a concern, I'd recommend this coil just because it's cheaper than theirs.
But like I said to begin with, it honestly sounds like a voltage drop or insufficient amperage when warm. If it's cranking slower it's probably not feeding the FI system the appropriate voltage to operate properly.
Gratuitous pic of my engine for reference.