Take one of the lines out of H36 and make it ring directly to a display phone and ensure the Caller ID is coming through.
If that works what you may need to do is make a dummy extension SLT or phone ring on the lines and then forward to the voicemail via the G-Screen forwarding program to get the delay. Even then not sure if the Caller ID will remain as like I mentioned earlier the Caller ID doesn't stay after the transfer. You can try to verify that with the line you make ring directly to a display phone. If the caller ID is there then transfer it to another station and see if it stays. I think the post you were mentioning about the Caller ID staying is when you have 3.0 software on the CPU and are using the PRI card with caller ID options set. On the Caller ID box if my memory serves me correct it goes away shortly after being answered.

mjc