I ended up getting the Panasonic phones I linked to in the OP. I received them today and got them all set up in the new house.
After I got the base station linked to my cell phone, and set it for "Cell Only Mode*", it was smooth sailing. Everyone I called said they could hear me crystal clear, and I had no trouble hearing them. While I've only had the phones for less than a day and made maybe 3 calls on it total, I can say I'm very satisfied so far.
* Using cell only mode means you lose features like the phone's built in answering machine. Since your cell phone more than likely has voicemail capabilities already, its no great loss.