Allow users to view and edit tickets from Related Objects

We currently have a many-to-many model, where our users belong to multiple organizations. The reason for this is that we support our clients and our clients' partners in one place. We need our clients to be able to support their partners. To be able to do this, we add all of our clients to their partners' organizations. 

We recently hit a wall where we reached the 300-organization limit for a single user and we need to find an alternative solution. 

I've been brainstorming and I came up with a possible structure, but still have a blocker. 

I create a lookup ticket field to an organization and filter it so that it only shows “client” organizations. When I view that client organization's profile, I see the linked tickets under the “Related” tab. 

It would be perfect if users could have permissions for related tickets. In this case, the relationship is set through that Organization lookup.

I think the only way to fill this gap now is with the API, but I'm not a developer and I don't have resources to accomplish this right now.