Socializing two lady cats. Do we let them fight it out?

I've had B for 10 years, I adopted her as a kitten. She's always been shy, doesn't like new people or loud noises. When she was younger and I was still living with my dad we introduced a new kitten to the house and it took her a while but she got used to him and they were best friends after a few weeks.

B was with my parents over the holidays while I was out of town. During that time my roommates took in a stray ~1 y.o. cat, aptly named Porch Cat. She's straight up the sweetest cat I've ever met. We got her vaccinated and spayed and we're looking for a home but it's slow going.

Once Porch Cat got a clean bill of health, we brought B back. It's been about a week. It's not going well. We're doing this dance, moving one cat into a bedroom so the other can roam the house for a few hours, and then switching them. They seem curious about each other but any time they get too close to each other (on opposite sides of a door with a ~1.5 inch gap underneath) they hiss and growl and sometimes bat at each other. If you try to pick one up when this is happening you get scratched. I've tried briefly to get them in the same room and it was clear there was going to be a fight.

Do we just let them fight? They're both incredibly sweet cats on their own, but I think they're both feeling very territorial and I'm not sure what to do. I'm going crazy! Any advice would be really appreciated, thank you!