You'll likely need to push the modified template from the ASA to the client to get it working properly. I set this up this morning and it worked wonderfully.
Since you've modified the AnyConnectProfile.tmpl with the necessary changes, upload that modified file to the ASA using the CLI or ASDM. A good place is just "disk0:/AnyConnectProfile.tmpl".
In the webvpn config mode, create a new profile using that file:
ciscoasa(config)# webvpn
ciscoasa(config-webvpn)# svc profiles MY-PROFILE disk0:/AnyConnectProfile.tmpl
Next, you'll need to associate this profile on either a per-group or per-user basis, or both:
ciscoasa(config)# username testuser attributes
ciscoasa(config-username-attributes)# webvpn
ciscoasa(config-username-webvpn)# svc profiles value MY-PROFILE
*OR*
ciscoasa(config)# group-policy my-vpn-group attributes
ciscoasa(config-group-attributes)# webvpn
ciscoasa(config-group-webvpn)# svc profiles value MY-PROFILE
The next time you connect with the AnyConnect VPN client, the new profile should be downloaded and applied immediately. The changes you made to AllowRemoteUsers should allow you to connect via your RDP session without error.
Good luck!
James