I had two Actiontec GT701s , one with wifi and one without, when I had Qwest DSL. I still use the wifi one as a wireless access point. I never had a problem with VoIP (Lingo). As I recall, you could configure the Actiontec to work in transparent bridging mode (RFC1483), PPPoE, and possibly even PPPoA. I don't know what Verizon supports, but Qwest supported all of those IIRC. VoIP worked fine in all modes, even PPPoE, which involved double NAT.

If you put the modem into transparent bridging mode, you can let your router do the PPPoE authentication. Because the PAP2T is not a router, it cannot do the PPPoE authentication. But for testing purposes, you could set up a soft phone on your computer and let your computer do the PPPoE authentication. This would avoid NAT altogether. Or you could do the same thing by using an ATA/Router and having it do the PPPoE authentication, with the Actiontec in transparent bridging mode. This would essentially allow you to take the router functions out of the picture for purposes of testing this problem.

All of this is pretty speculative, since I don't know how Verizon is set up. But I do think the Actiontec is configurable enough to let you figure out whether this problem is caused by the router function of the Actiontec.