In a roleplay that I'm in we use non-linear, timeline-based posting that allows us to interact with one another and progress the story without having to wait for people or adhere to a specific posting order. While we are urged to post once a week, it's not a big deal if someone has other obligations that prevents them from doing so. Just putting this out there, might be a solution that could suit your needs!

This, of course, can make the posts quite extensive depending on how much you want to contribute and how many timelines that are currently active. But, we are urged to plan our posts whenever time allows it by writing notes in our phones, on a piece of paper, or whatever! For me, it facilitates the writing process as I already know exactly what I want to write!

Anyway, I hope that you find a solution that you're comfortable with!