I'm beginning to think one of your cams is out of time. Each cam has a "number 8" reference mark, where the "number 7" in the diagram is for the oil pump shaft (number 1). Did you verify that the #2 piston was at TDC when you rotated the cams to time? That's the crank reference. With all the backfiring and rough running you could have maybe two pistons out of time even, hopefully though it's just a pair of valves. I'm not intimately familiar with the 6VE1's sequence so am just generalizing.

If it were me I'd re-time from scratch using the Service Manual procedure, letter for letter.