If you have to tap the starter to get it to work, common sense points to your starter. I've worked on cars since '99, and do you know how many NEW parts I have put on have turned out to be faulty? Especially re-manufactured parts from Advance or Autozone.
The palladium brand has a particularly high failure rate as a new part. The reason the starter works when you tap on it is because you are releasing the switch in the relay that is mounted to the top of the starter. No ifs ands or buts about it, if you are tapping on the starter to get it to work, and it works, your problem is associated to the starter.
It sounds like your starter is having heat related failure as it won't start after youve been driving for a while, but it will if you havent drove in a while.
Try shimming your starter. When they recondition starters they shave the deck of the starter and some times they take off too much so you have to shim it.
I cant really gove you an answer,but what I can give you is a way to a solution, that is you have to find the anglde that you relate to or peaks your interest. A good paper is one that people get drawn into because it reaches them ln some way.As for me WW11 to me, I think of the holocaust and the effect it had on the survivors, their families and those who stood by and did nothing until it was too late.