Your fuel pressure indications are key to your issue here.
At WOT, fuel pressure should be a steady 36 PSI. If fuel pressure drops during WOT then you are not getting adequate fuel supply to the injectors, that will cause the popping out the intake, (lean misfires caused popping out of the intake, rich misfires cause popping out the exhaust).
Typical causes for dropping fuel pressure, in order of priority to check;
1) Clogged fuel filter, (They're cheap enough, should be changed once a year any how).
2) Clogged inlet screen to the fuel pump. (Remove the large fuel hose, look inside the inlet of the pump, you will see and inverted cone type screen, which will get clogged up with rusty tank debris).
3) Fuel pump going out, (usually because of clogged inlet screen).
4) Crimped or restricted fuel supply hose/hard line, between the tank and injectors. Visually inspect all the fuel hoses and metal lines for kinks, crimps, dents, etc. Small dents in the lines usually aren’t an issue, it will take a noticeable pinch to cause this.
5) (This is a feeble stretch, but “could†happen I guess). Poor electrical connections to the fuel pump not allowing the pump to get full power.
Hope this helps, keep us posted on your findings.