So I ran a +11 Halls of Atonement just now where our tank had to pop out of the instance for a second after the start to change specs due to forgetting to switch out of Mistweaver before the run started. This has resulted in this log: Summary - Last Pull - Report: Mythic+ Season 3 | Warcraft Logs which says that we ran it with zero tanks but two healers, one of which did the best damage any Mistweaver had ever done for that key level but absolute dogshit hps.
I get that dungeon logs/parses will always get weird with a mid-run spec change, but I think it makes sense that if a character was clearly the same spec for every single combat encounter of a run but not that spec at the very start the system should count them as the spec they fought as, not the one that they started as.