Wouldn't have worked. Centers handle aircraft over several states, most of which are too far away to contact directly.
I don't doubt that was the problem here. The remote radio relay system crapping out.
At altitude, you can easily reach another airliner 200 miles away.
I'm only a private pilot, but I have relayed messages from ATC to other aircraft before. It works.
Also, the first thing the airliners should have done was to contact somebody - anybody - and have them call ATC on the landline.
As a last resort, they fly the flight plan as filed, weather permitting.