Hello,
I'm having an issue getting Exchange 2013/2007 coexistence working correctly.  My customer has Exchange 2007 SP3 RU15 on Server 2008, and a new Exchange 2013 CU8 on Server 2012 R2.  We are migrating on-premise to Office 365.  All production mailboxes reside on Ex07.  

I have not switched any production DNS records thus far, and am using only HOSTS file to test proxy/redirection.  Here's what I am seeing:
-OWA: redirects from Ex13 to Ex07 fine.
-ActiveSync: proxies from Ex13 to Ex07 fine.
-Autodiscover: will not proxy from Ex13 to Ex07 using default authentication methods.  Getting 401 errors.  I am able to get around this by using Basic Auth, but it's not ideal.
-EWS:  If a user attempts to browse to https://autodiscover.company.com/ews/exchange.asmx (which using HOSTS file is pointed at Ex13 CAS), the user is presented a login popup.  An Ex13 mailbox user enters credentials and sees the content on the page.  An Ex07 mailbox user gets the same login popup, enters credentials and the login popup reappears and the user will never see the content on the page.  Getting 401 errors in the IIS logs.  If the Ex07 mailbox user browses to the server name instead -https://<servername>.company.com/ews/exchange.asmx - the user can successfully authenticate and see the content on the page.  This is pretty similar to what I was seeing with Autodiscover prior to changing the auth methods.

This EWS authentication issue I believe is now causing Ex07 mailboxes free/busy and calendar lookup issues to O365 as the AvailabilityAddressSpace URL matches the EWS URL of the Ex13 CAS server.  An Ex13 mailbox can view the calendar for an O365 user just fine.

As a sanity check, I mirrored this environment in a lab, and all the above things work as expected.  I have validated all vdir permissions and authentication methods from the lab to this production environment.  

Ex07 mailbox user EWS request to https://<servername>.company.com/ews/exchange.asmx
2015-05-27 12:41:27 172.26.217.243 GET /owa/auth/logon.aspx url=https%3a%2f%2fservername.company.com%2fowa%2ffavicon.ico&reason=0&CorrelationID=<empty>;&ClientId=Q0EUOYGUKQJGSTPB0XA&cafeReqId=61e24644-f9a9-4f4e-bc04-e3a377b6cc71; 443 - 172.16.1.31 Mozilla/5.0+(Windows+NT+6.1;+WOW64)+AppleWebKit/537.36+(KHTML,+like+Gecko)+Chrome/42.0.2311.152+Safari/537.36 https://<servername>.company.com/ews/exchange.asmx 200 0 0 218

Ex07 mailbox user EWS request to https://autodiscover.company.com/ews/exchange.asmx
2015-05-27 12:54:37 172.26.217.243 GET /ews/exchange.asmx &CorrelationID=<empty>;&ClientId=YESMUJEYHGEURVYKGOA&cafeReqId=8353452f-7e09-4aef-bcb6-a85fbe69edc0; 443 - 172.16.1.31 Mozilla/5.0+(Windows+NT+6.1;+WOW64)+AppleWebKit/537.36+(KHTML,+like+Gecko)+Chrome/42.0.2311.152+Safari/537.36 - 401 1 2148074257 6500

Ex13 mailbox user EWS request to https://autodiscover.company.com/ews/exchange.asmx
2015-05-27 13:04:48 172.26.217.243 GET /owa/auth/logon.aspx url=https%3a%2f%2fautodiscover.company.com%2fowa%2ffavicon.ico&reason=0&CorrelationID=<empty>;&ClientId=YESMUJEYHGEURVYKGOA&cafeReqId=21b324ee-320e-43e3-bb7d-443a45bd53ac; 443 - 172.16.1.31 Mozilla/5.0+(Windows+NT+6.1;+WOW64)+AppleWebKit/537.36+(KHTML,+like+Gecko)+Chrome/42.0.2311.152+Safari/537.36 https://autodiscover.company.com/ews/exchange.asmx 200 0 0 15

I'd appreciate any thoughts.  Thanks in advance!