For what it's worth, *67 doesn't actually block anything. When you receive caller-id, you're getting CPN; it's one of the two ANI fields your switches passes. What it does do is add a bit that's transmitted along with those two fields, instructing the switch not to give it to subscribers. For the most part, that's all you need, though; one of the biggest problems you'll have are people calling back and going OMG BRO Y U CALL ME????????//. A lot of residential lines come with anonymous call rejection service now, so usually that doubles as a good way to avoid ringing their phones.
The other problem is slightly more serious; PSAPs. Basically, they're regular numbers that forward to 911. The county you live in will probably publish at least a good few of them; do a search for "(your county here) county public safety answering point", or something along those lines. Tell your wardialing software to skip over them if they're in the exchange you're dialing. To be safe, you could probably also skip 0911, and 9111 in the exchange you're dialing as well, along with any published police/fire/hospital numbers.
Back to your problem with the modem, though; if *67 works for you dialing normally, there's no reason why it can't work for your modem. To the switch that processes your phone calls, it literally looks no different then a normal person picking up the phone and dialing. You'll want to look for options similar to the "dial an outside line code first" thing in your wardialing software instead of the Windows modem settings box. If you're using a phone line from Centurylink, there is a way to spoof CPN from it pretty easily, but it involves call forwarding and one of the anonymous call rejection IVRs. It'll slow your wardialing process down to a crawl, so probably not practical in this application. If you'd like to use it for normal calls, here's how you do it;
1) Forward your calls - using selective call forwarding or whatever you may have available to the number you want to dial
2) Call the update center; *78, or 888-(your area code)-8052, and make sure anonymous call rejection service, or whatever they call it (it'll be the third feature in the menu) is enabled
3) Dial *67, and dial your own phone number
4) You'll get a recording saying the number you're calling doesn't accept unidentified calls. You'll be given the option to enter the number you're calling from.
5) Holy shit, it spoofed!
Just keep in mind, there's two anonymous call rejection services. One of them you enable with a *xx code; there's no option to enter your own phone number there, so don't use that one.
As for telco security? As someone who has done quite a bit of handscanning from quite a few phone lines, I'm pretty sure they don't care. Unless you're harassing people or performing some kind of fraud, you probably don't have anything to worry about.
That being said, pick up the phone you're going to be wardialing from, and dial 1-700-555-4141. You'll probably get a recording saying something like "Thank you for using Shadytel Long Distance". If the recording you get says anything about MCI, you may want to avoid wardialing from them; that's the one long distance carrier I've heard actually complain to someone about sequential dialing.
Other then that, have fun! There's a lot of cool stuff out there to find. There's plenty of modems out there, but just keep in mind you'll hear a lot more if you're listening with your own ears, and choose very specific parts of a range. Look into hand scanning if you're curious.