Exchange 2010 Autodiscover DNS configuration

I'm unable to get the Autodiscover of Exchange 2010 working. Our email accounts are name@company .com and our AD is company .local

When I open Outlook 2010 and Ctrl + RMK on the icon and select 'Test E-mail AutoConfiguration' I see this:

 SMTP=myname@company.com
Attempting URL https://exchange1.COMPANY.LOCAL/Autodiscover/Autodiscover.xml found through SCP
Autodiscover to https://exchange1.COMPANY.LOCAL/Autodiscover/Autodiscover.xml starting
GetLastError=12007; httpStatus=0.
Autodiscover to https://exchange1.COMPANY.LOCAL/Autodiscover/Autodiscover.xml Failed (0x800C8203)
Autodiscover to https://company.com/autodiscover/autodiscover.xml starting
GetLastError=12029; httpStatus=0
Autodiscover to https://company.com/autodiscover/autodiscover.xml Failed (0x800C8203)
Autodiscover to https://autodiscover.company.com/autodiscover/autodiscover.xml starting
GetLastError=12007; httpStatus=0.
Autodiscover to https://autodiscover.company.com/autodiscover/autodiscover.xml Failed (0x800C8203)
Local autodiscover for company.com starting
Local autodiscover for company.com Failed (0x8004010F)
Redirect check to http://autodiscover.company.com/autodiscover/autodiscover.xml starting
Srv Record lookup for http://autodiscover.company.com/autodiscover/autodiscover.xml Failed (0x80072EE7)
Srv Record lookup for company.com starting
Srv Record lookup for company.com Failed (0x8004010F)

If I go via my browser on a client pc to:

https://exchange1/Autodiscover/autodiscover.xml

I see an XML reply (so I guess this is the autodiscover URL that should be used) (exchange1 is the servername.). This is what I see in my browser:

  <?xml version="1.0" encoding="utf-8" ?> 
- <Autodiscover xmlns="http://schemas.microsoft.com/exchange/autodiscover/responseschema/2006">
- <Response>
- <Error Time="15:21:30.8211336" Id="2980235674">
  <ErrorCode>600</ErrorCode> 
  <Message>Invalid Request</Message> 
  <DebugData /> 
  </Error>
  </Response>
  </Autodiscover>

When I try this:

  https://exchange1.company.local/Autodiscover/autodiscover.xml 

It ask for my username / password and if I enter them I see the same XML message. Now on my DC in the DNS Manager I have this:

DCSERVER
- Forward Lookup Zones
-- _msdcs.COMPANY.LOCAL
--- dc
--- domains
--- gc
--- pdc
-- COMPANY.LOCAL
--- _msdcs
--- sites
--- _tcp   <---------
--- _udp
--- DomainDnsZones
--- ForestDnsZones

Under the COMPANY.LOCAL > _tcp I have added an SRV record:

_autodiscover    Service Location (SRV) [0][0][443]  exchange1.company.local    static

Could anyone see what I'm missing or misconfigured?

Update:

1) Get-AutodiscoverVirtualDirectory

Gives me:

Name                                    Server                                  InternalUrl
----                                    ------                                  -----------
Autodiscover (Default Web Site)         EXCHANGE1

Looks like I need to set an InternalUrl also. Is this correct?:

Set-AutodiscoverVirtualDirectory -Identity 'Autodiscover (Default Web Site)' -InternalUrl 'https://autodiscover.company.local' 

2)

in the DNS Manager, I only have an SRV _autodiscover Record in _tcp as said in this post. Is this enough? Or should I add an A record with these settings in 'Forward Lookup Zones > COMPANY.LOCAL'?:

Name: autodiscover
Type: Host (A)
Data: <ip of exchange>

What about on the Exchange side...what are the internal/external URLs configured as? Do you have an A record in DNS for "autodiscover.company.com" (or autodiscover.company.local internally) and does your SSL cert have both names listed?

Set the internalURL and create an A record...both internally and externally (using autodiscover.company.com) if you want the clients to be able to autodiscover from outside too.