Thanks everyone for the info here. I recently purchased a 2014 S7 with 80k miles and have the exact same issue. Dealer was no help (other than confirming that the ECU update had already been done). And my independent shop was pretty stumped. First tried evap valve replacement, which seemed to help mitigate the issue. But still present. Then I bit the bullet and had both HPFP's replaced ($1500 parts and labor). Car runs much better across the board and have not had any trouble with starts so far (knock on wood). But have only had it back a day and will update if it happens again.