It would be interesting to know what the BT Advanced Phone Z would do on my Sky VoIP line, my guess it would display 01 and 07 for caller id. If the OP has some way to test this it would lend weight to any case.
I have had the impression for some time now that IDNet are not interested in domestic customers and will do the minimum possible to get them off the line. There is currently an altnet cabling into the village (which means that BT have also suddenly announced that we are now in the FTTP plan). As soon as we have a viable alternative I'll be moving away from IDNet.