I know it's way too late, but from what I recall - Alastor used Legilimency to bend Harry's mind to become person who is hurting (even if for a short period of time). Imo in the universe the Legilimens can force their mind onto another by breaking their will and then put whatever character the Legilimens wants in their place
It still could imply that Quirrell/Voldie was an Heir of Slytherin - Harry hadn't actually "willed" the Animagus Voldie to speak yet, so him talking in Parseltongue could still be a clue. Or I am just mistaken and Harry had "consented" snake to speak in some way before