Cox Compatible Telephony Modems

In a search of the forum for issues about replacing the free cox modem that comes with using cox phone service, I read the following reply from Cox:

"Andrew is correct in that you may not purchase a telephony modem for Cox use. We do provide telephony modems at no cost for the time you may be subscribed to Cox Phone Service."

I was looking at the possibility of buying a compatible modem to improve performance since I want a 16x4 or higher device because the free Cox modem 8x4 doesn't offer the performance I need.  

I see in the list of compatible modems two that DO have telephone ports, the ARIS Surfboard TG1682 and the TG2472.

Will these not work with Cox phone??

Ray