I am using Auto discover service Url for a specified e-mail address.
ExchangeService Service = new ExchangeService(ExchangeVersion.Exchange2010); Service.Cr
I have used direct:
Url = new Uri("https://outlook.office365.com/EWS/Exchange.asmx")
and it worked for me. You may try use Fiddler and eM Client to see how they use EWS Managed API to get things done and replicate calls.
EWS Managed API