Any thoughts on this engine issue

I read through the entire thread but have lost track of what you have done.
#1 when you had the #1 @ TDC did you check/Mark the balancer?
#2 either something is wrong with your timing light or there is an ignition problem. The light SHOULD NOT skip like that try another light - if the same there is definatly an ignition problem.
3# do you have the vacuum advance hooked up to the ported vacuum on the side of the car? If so get rid of it for now.
#4 Make sure your ignition Box has an EXCELENT ground - the box case should be grounded - clean off the paint behind one of the bolts.
#5 if you think it could be a mechanical distributor problem you can drill some holes in the top of the cap @ #1 terminal - big ones - then you use your timing light to watch the position of the ignition rotor - this assumes you get a nice steady flash from the timing light.

#1-- No need to the marks lined up when we did this.
#2-- Light is definitely good working light -- Which we all agree here it is an ignition / electrical issue for it to jump then
#3-- We did both -- No change -- you can read previous pages of how it runs when we create a deliberate vacuum leak.
#4-- It appears to be good -- maybe I will add another ground strap just to be certain
#5-- I don't think it is a dist problem since we have changed the dist a couple times.

Welcome to the great 340 shake dilemma.... much has been tried.... I think hot wiring it next is the best option to rule out the dash harness.