You can't send calls to a pickup group, so I am a little confused... Do you mean hunt or ring group?
But I think you are overthinking this, the end result is to ring (queuing) the receptionist for ~30 seconds, giving a comfort greeting at 15s, then going to a "group". An ACD Express path may be best. Create an ACD Express path with the receptionist extension in it and ring for 30-45 seconds, and play an announcement at 15 seconds, then if no answer recall to the hunt group.