I feel that between-game actions can follow one of two possible paths.
Any between-game action system consumes a huge amount of staff time and distracts from the actual game being run over the weekend.
Blades in the Dark has a downtime system.
Unpaid
Honestly, this is my preference. In many ways, people already do this by engaging in ad hoc roleplay in whatever manner they can manage. If this is included in your POLAR membership, it would happen more often and might overwhelm your staff.
Paid actions
This would further separate low-income players from the rest of the group.
I am convinced that most of the appeal is that the “work” is fun. So, let’s get paid to do fun work!
If the plan is to make money doing this rather than simply covering costs, I’d be curious to know how much money you have in mind. You would need to stop doing this sort of thing for free for your friends if you charge for it.