I had the cap not getting a good seal or something. It must not have been as bad as yours since it never cut off. It just had a hard time starting while or after it rained and to get it started I would have to do like you did and almost floor the accelerator and it would start. The old cap looked fine so I guess even the smallest thing could make it not do right. I also replaced the rotor cause I hear it's best to replace both at the same time.
Oh and your problem with shops is the reason I only like 2 or 3 places around here even touch mine. I always want to do my own work, but I'm bad at troubleshooting and sometimes something it more than I'm able to do so I have no problem paying a shop to do something I'm not able to as long as I can trust them. I had one shop I used to go to and I caught them lying to me so that did it for me. It's 2 shops and one alignment shop that I like work on my truck, the others I don't mess with.