Does the drawback only apply to the initial roll or also to any rerolled dice? If I roll Hit + Hit + Blank + Blank and reroll the Blanks and get Crit + Focus do I then change the Crit to Hit?

Every time you ROLL a crit with the HLC immediately change it to a normal hit, even on a reroll. You can however use other abilities to modify a die to a crit. Mercenary Copilot and Marksmanship being the notable ways to do so.