I'm fairly certain the missionary quick kill isn't random, I used to think so but now I get it like, 90% of the time. If you see in this video here: You have to try and wedge yourself very close to his side/back, animation cancel shoot, and then make sure you dont let go of aim, walk up until she aims downwards, then fire. The RNG for me is where he will decide to move at the start of the fight. Can't say this will work for everyone but it's what I do right now.

From what I can see in your PB vid, you're not close enough to Alessa. You have to walk up to her so much that you're touching her really, then animation cancel shoot, then shoot slightly to the left (don't let go of the aim button, for me it works if I just hold left before the next shot is even ready, then tap fire as opposed to holding it). If you're using the easier method for the first phase, you definitely don't want to aim left, I'm not sure why you aren't getting two shots with this method but it's largely based on positioning.

Speaking of not letting go of the aim button, make sure to do this on the last phase of the fight too, after you shoot her to the ground do not let go of aim, then walk over to her and Heather should automatically aim down, then you can shoot. Doing so usually results in the quicker last phase for me.