I have a 05 Gt with the same exact no start issue as you had. I tried what you put in your thread and it cranked once, but I haven't been able to get it to do it again. Did you end up replacing any parts on yours?
Yeah I swapped a T-5 in last summer, welded in subframe connectors, just put in new Tokico blue shocks/struts, got new exhaust from the mufflers back (wife said it was too loud for our 1 year old), and put new chrome 93 cobra wheels on in Feb or so.
Took it on Hot Rod Power tour this summer too. Got 22-23 mpg!