SharePoint and Teams: Better Together

My workplace is all for embracing innovation and keen to find better ways to collaborate and we really see the potential for using Teams. We have created a Team and want to utilise the associated SharePoint site for working document records management and collaboration, the benefit of cloud based storage and also as a departmental intranet. The issue I am facing is that if I create unique permission groups in SharePoint it makes no difference as the Teams permission (either owner or member) overrides it. We would like to limit page editing and publishing to a few staff in SharePoint. Many staff have the Owner permission in Teams as we are now utilising Shifts for rostering and only owners can edit the roster - these people are our supervisors and line managers. In testing the associated site I have already run into issues of staff inadvertently breaking the home page and wreaking a bit of havoc. I have limited permission to site pages as read only for all users except the SharePoint owner group, however and again, the Teams permission overrides this and the edit page option is still accessible to Teams members and owners. I have read that you are unable to modify the default member permission in SharePoint, but just wanted to check that this is actually the case, and if anyone has any suggestions for how we can achieve the desired outcome of a structured and well administrated SharePoint but still make the most of the collaboration features in Teams and still have staff able to utilise Shifts to do rostering.  Thanks.