Using a 50 ft. RJ11 extension cord on the Chattaway and the T10. I get buzzing with both of them.

Not much we can do hear, but you can try 1 thing:

Use (2) 25 ft. RJ11 cords with a coupler. It will give you 50 ft. without the buzzing, and it works for both the Chattaway and T10 units.