Geekette, try running a few tests
here,
here and
here. I suspect there may be noise on the lines and you may have to yell at your ISP. To help leverage that yelling or noise line issue diagnosis, you might want to take advantage of
this tool as well, it should help isolate whether it's line noise or over-sold bandwidth or routing issues on the ISP end.
Also, it might not hurt to try and run all those things without your router in place as well, just in case
it might be the cause. Just be sure to fully patch your OS and use a software firewall like
Comodo first.
Don't worry about the wiring in the house, that's not going to impact the end you're having trouble with, and the VOIPo folks just say that to reduce support issues and ensure your device won't get fried. If you've got the wiring disconnected at the DMARC and properly tagged as such with equipment warnings in the box for the phone company to see, you should be fine.
As for the additional rings, that's something a lot of ATAs will do if there's handshake/connectivity delays... the ATA will ring like it's connecting while the actual connection is still being negotiated so you don't just get dead air and wonder if the call is going through.