There's a way to do it that you've likely never considered
I’ve often used positive self talk to get me through tough workouts and practices but not as a conscious training tool or in a “reward the work not the finish” point of view, so I’m going to pay more attention to the words in using in the moment and how I can adjust them.
Incidentally, I much prefer to ask athletes how they felt about their race rather than their finish result. One, because I think empty praise of a finish result is lazy but also because I think that athletes should be more focused on how the race went rather than the finish. I suspect this is closely related to what you’re discussing here.
Also, don’t beat yourself up about whether multiple plunges versus 5min sustained submersion “counts”. In water that cold, had you forced yourself to stay in for 5min would almost certainly have resulted in hospitalization due to deep hypothermia. You wouldn’t have easily re-warmed in the trailer.