tl;dr: is a slightly ajar door a good way to introduce cats that have been playing with each other under it without showing aggression?
We have two cats, neutered - the male is the resident house cat and the female is my brother's, who came home for the summer.
They play a lot under the door and don't show signs of aggression when doing so, although the male has shown signs of feeling threatened by the female in the past (single encounter a week ago and a couple months ago). I already asked a question trying to discern if they're playful with each other or just toying with the door here and I feel confident they can get along, if they meet properly and slowly.
We've been thinking of using the door, by opening it just enough so they can see each other and get close enough without being able to paw at each other (the door being slightly ajar enough for looks but not claws) as a means of taking their introduction to the next step, safely. I'm thinking that's a good idea as we can just shut the door if they get too agitated, they'll both have escape routes, they won't be so afraid of each other and any interference by us (namely, shutting the door) won't get us directly involved, thus making them feel we're getting in the way. In fact, I thought of doing it while they're playing under the door, so that it'll be easier for them to identify what cat they're looking at.
However, we're also worried it might agitate the male because he won't be able to enter. I think it won't be a bigger factor than his fear of the female, but we're unsure.
Is this a good way to further the introduction or is it more detrimental to them getting along than helpful?