Consider that the people working for you are experts, but the rest of the world on average is not. If one cannot make a judgement whether <https://eprint.iacr.org/2004/207> weakens SHA-2 for a particular use case or not, then it is safer to assume the worse, and simply use SHA-3 instead.
This is tangential, but your facts about tptacek might be a bit out of date. He's no longer at Latacora; he's now working at fly.io. So I think it's safe to say he has recent experience working with people who, while they're skilled developers, aren't security experts.