HI,
My (very old, first installed in 2000) system of Beocom 6000s also comprises a base (original type) and four handsets. Occasionally one of the phones will give in engaged/busy tone and it proves impossible to reset. I would try turning it off and on, off and leaving it overnight and then turning on, even removing the battery. I would still get the same busy tone. I even tried deleting the handset and reinstalling.
Finally I solved it by just turning off the base unit for a couple of minutes and then restarting. This has happened three or four times now and the base unit restart has worked every time. Not sure if that's the same as your problem or whether this solution works all the time but it did for me!
Best regards,
Pete