I have a couple of questions.
I do believe Tech Electronic has addressed part of your question, but possibly not all of it.
If I understand you question correctly, it sounds like your old Telco carrier allowed Customer provided CLOP (Call Line Outbound Presentation) as the originating caller ID across the PRI that you are using as your outbound trunks (forwarding an extension to a cell shows the main number), this feature is important especially if you have IP phones at remote locations so they can send out the correct 911 info.
By default, Telcos don't allow this feature unless specifically requested and sometimes it is an additional charge, by default many only present the billing number as outbound caller ID presentation and this sound like your case. You may be able to get hold of your telco and request their data-base administration modify the PRI to allow this feature.
It sounds like your systems are networked together, are you using T1/PRI or IP for your private network?
thanks, Jim
Are both your