Different way of working
Some of the restrictions that you mentioned and the usability of the Office365 solution is designed to work in a different way to how an organisation works.
An example would be: if you email out a weekly newsletter to all your members of staff (and you have a significant amount of staff) then your organisation is not thinking in the right way for 'cloud' computing.
With massive circulars like this an intranet site with audience targeting maybe better suited as provided with Office365.
If you want to replicate exactly what you had before then you will need experts to replicate and manage it for you, as you did before.