To anyone seeking to beat this record: YOU HAVE TO SCORE IN RUGBY SEVENS, as well as in the Duel variation. The reason being is that each mode must be played until completion, win or lose. If no one scores in the two halves of Rugby Sevens, it will go into overtime and two more halves are played. Both of the records that had "beaten" my time on SRC previously were guilty of exiting out of the mode before any points were scored at the end of the 2nd half, thus they weren't truly completed. Since scoring takes a few extra seconds to process, it also affords an unfair time advantage. It's odd because this mistake was not made on either of the Football modes, but nevertheless I'll reiterate it: you have to score in Rugby Sevens.
Anyway, for this run, I switched to running the game digitally directly from my Wii U's NAND, shaving off some load times. In addition, I found a faster and more consistent way to lose Beach Volleyball. I also probably had my best time in boxing yet.
Weak points: Bad starts in 100m, 4 x 100m relay, and Equestrian. Also held the ball too long in Duel Rugby Sevens during additional time. Nothing major, but I could've been a lot closer to sub 34 if I hadn't made those mistakes. I think a sub 34 is definitely possible.
You have to score in Rugby Sevens.