centurygarageI enter my URL: intranetinitiatives.sharepoint.com (P1) and get a https://intranetinitiatives.sharepoint.com/SitePages/Home.aspx
which is a (E3) Team Site home.
No, it's not. In a P account that's a wiki page within the public site collection that's created by default. Either you set it at as the home page of your public site or it got corrupted (which seems to happen to a lot of people). Unfortunately the option to reset a public page as the home page was disabled in the ui by MSFT so you'll have to do it in Sharepoint Designer.
Open the site All Files>>Pages>>highlight default.aspx and click "set as home page" in the ribbon.