Hi @pitz that was a great outline of what you wanted, thanks for being so detailed.
The issue currently with Webflow Memberships is the lack of association between a Membership and the CMS. They are two separate things not linked to one another.
So to make it all work you have to create that link.
With an open mind and a little bit of effort it’s totally doable.
Here’s the high-level overview (if you’re interested):
When a membership is created or updated you get the user id.
You tap into that functionality by creating a Webflow Webhook.
You can send that Webhook off to a glue service like Zapier, Make (Integromat), or even Webflow Logic to do what’s next…
Now you need to associate that user id to something in the Webflow CMS. The most common approach is by using CMS Collection Pages.
They give you a slug that’s associated with each item in the CMS. For example, if you had a users CMS Collection it might look like this:
https://site.webflow.io/users/bob-smith
The common approach has been to “hide” that item by replacing the slug bob-smith with something unguessable.
For example:
https://site.webflow.io/users/45Rtf873Ds298Gvbfh40oiT
Ugly indeed 
but this gives you what you need and that can be automated via your glue service.
Next, you password protect that CMS Collection Page behind the memberships feature. Only logged in users would ever have the chance at guessing a users project page / dashboard, which is highly unlikely.
Now this user can create & update projects and that projects CMS could be public (e.g. not gated behind Webflow Memberships).
Through your glue service you can also take the users dashboard link (https://site.webflow.io/users/45Rtf873Ds298Gvbfh40oiT) and add it to their Memberships account page.
Membership account pages are only accessable by the currently logged in user (Webflow handles that for you).
When a user logs in, they go to their account page and click into their user dashboard / project page.
As Webflow backfills some of these features that you’re forced into manually creating, you can incrementally remove them.
Another option is to skip Webflow Memberships for now and use something like Memberstack which gives you the flexibility you’re looking for out of the box.
Here’s a screencast walking through what you’ve asked for:
(if you dig around on the site you’ll find a bunch more)
Hope that helps!