Welcome to Meta, @waffleslop!
I think everything you listed is 100% possible with Discourse and some sort of membership plugin.
You may not need that whole dependency stack there. I run a personal productivity community using Wordpress, Paid Memberships Pro, and Discourse. I’m finding I’m slowly drifting toward wanting to use Discourse for more and more things and the WP/PMP side less and less. That’s probably partly because I do Discourse development, but also because Discourse is just a fantastic piece of software.
Have you looked at ProCourse Memberships? It’s possible this could fit your needs. You could restrict all categories to a members-only group that way. The only downside is at this time users can purchase a level via ProCourse Memberships after they have an account (vs. before, which is what it sounds like you’re after).
Discourse will be able to handle 1500 users easily. If you host somewhere like Digital Ocean, scaling it is very straightforward – just upgrade your droplet size.
For most of your requests, you may want to hit up #marketplace to chat with developers to help you with any custom projects you have.