Percolation? Heat soak? Don't drive during summer??

Doc, plenty of comments - plenty of good info, one positive thing that you have going is you seemingly can stay at the house and have the problem so no tow truck calls - any time someone has a crazy issue the 1st recommendation is to not throw parts at it which is always good, also new parts these days do not mean good parts, below is my .02 worth

make sure you have a fire extinguisher close at hand

find and fix the issue with the weird spark comment - may not be the main source of your problem but it is a problem

try to find tech info on your electronics (coil, ecu, etc) for cold and hot readings - check all the values you can confirm, when the car shuts down check resistance values on everything for spec, this is tricky because temp affects things

Jpars comment for a trickle of fuel may or may not work depending on how little a trickle you add, not enough it could vaporize and you wouldn't know if it was an issue or not - this is tricky (hence the fire extinguisher), may take more than a small trickle

the comment about dirty residue in your old fuel filter could be a sign of the issue - several thoughts - I know some of the old Fords I have worked on have a sock on the pickup tube in the gas tank, I had one that would load up when driving, after setting it would sort of clean itself somehow and then would be back to allowing enough gas flow to start and run - sort of last check but get some fuel line and a spare gas can - when the car won't start pull the fuel line and run to gas can - have someone turn the engine over while watching what is coming out - this could help to isolate a fuel pump/system problem. I would suggest doing this with the engine cold so you had a comparison of what fuel flow looked like before it was hot

it seems you have replaced several things in your ignition system - as mentioned in many places new parts are not necessarily good parts, with old cars it is not uncommon to have a new issue coincidentally - ballast resistors are the cheapest thing and fairly quick to replace and from what I have learned since owning my Dart is these are very common problems

recheck all of the electrical connectors that you might have removed are touched during your work - each time an old connector or wire is touched it could cause a problem that adds some extra resistance in a circuit that isn't expected. It is very easy to overlook a small issue when doing the amount of work you did when changing the cam.

As mentioned you have the benefit of having the car at home, when the car quits check one thing at a time, its easy to overlook what you need to do on multiple things when in a hurry, let the car cool then check the next thing, since you don't need the car to use daily, you don't have tons of money to throw at it, patience and some testing everything is just what you need.

good luck in the quest, everything mentioned could be the root cause of your issue, ruling out one thing at a time is gonna be the best path