Thanks for your suggestions. I tried the Call Routing and made some discoveries. I had to not have my number marked as private (my voipo) to get this part to work.

But I noticed, out of the options, there's not one that just blocks caller ID info. I tried Blacklist and it just gives a "call cannot be completed as dialed" error.

The other options are forward, send to voicemail, busy signal, whitelist; terminology varies depending on whether you're controlling outbound calls or inbound calls.

So, there doesn't appear to be a way to not send voicemail info. to those people who have private numbers.

Unless I've missed something of course.