I'm curious whether the following will work, although I'm not in a position to test it. (Steps 3/4/5 borrowed from another forum)
(1) change system-parameters features (the following was on page 9 for me)
CPN/ANI/ICLID PARAMETERS
CPN/ANI/ICLID Replacement for Restricted Calls: 001122
CPN/ANI/ICLID Replacement for Unavailable Calls: 001122
(2) change trunk-group xxx (the following was on page 3 for me)
Replace Restricted Numbers? y
Replace Unavailable Numbers? y
So now those calls with no caller ID will instead have caller ID '001122'
(3) change cor 995 (or some other COR you're not using)
Calling Party Restriction: origination
(4) add station 1234(or some dummy extension you'll never use)
COR: 995
(5) change off-pbx-telephone station-mapping 1234
Application EC500
Phone Number 001122
Trunk Selection ars
Config Set 1
So now 001122 calls will "map" to extension 1234, which isn't allowed to originate calls. So the call fails.