Gave up on my idea of connecting an analog cordless phone to a Linksys PAP2T and then to an AG310, and bought a Gigaset A580IP phone instead. Spent several hours trying to connect to my 2talk and Faktortel VoIP accounts, but to no avail. The phone has been issued a local IP address from the Linksys AG310 DHCP my home network and seems to talk to the base station, but that's about it. Nothing seems to get past the base station. The phone base station is connected to an ethernet port on the AG310.
If there is someone out there who uses either of these two providers, and has a Gigaset A580IP, I would be grateful for your words of wisdom in setting this thing set up. I should point out I'm not a complete novice as I have managed to set up softphones on my PC and iPhone to connect to 2talk and Faktortel, but obviously not yet an expert on these things.
One piece of information that may be relevant: my AG310 is locked down by VFX.