I haven't got a handset set up here at home at the moment in TW mode, but some stage over the weekend I'll grab one out of the car and test it, as the provider connectivity shouldn't make any difference to this sort of thing, as the SIP header will contain the calling party, so from there it is up to the system what it does with the number.
Out of interest can you paste the COS settings under display for the trunk and the handset?