Faulty phone has everything all the other phones have with one exception--twinning. Three call appearances on all phones.
Westi, I tried that, however putting a call in the group involved hitting transfer->dial->hangup.
I was looking for a one-button approach, ala "Park Call". The closest I got was to Enable_OTT on the user under source numbers and then create a dial button as you suggested, however in playing with it, I would end up putting the call on hold instead of queued into the group.