A follow-me hunt-list supports some options to configure behaviour.
The following options may be useful:
a- Record the caller's name so it can be announced to the callee on each step.
d- Disable the 'Please hold while we try to connect your call' announcement.
I- Ignore any connected line update requests it may receive on this dial attempt. This will prevent local handset forwards from impacting call flow
N- Don't answer the incoming call until we're ready to connect the caller or give up. This means the incoming call will hear network ring-back, and not be charged for the call until the recipient confirms they want to receive the call.