Very nice!! Thanks for that output, and clever hackery to make it happen! You can also do that on the command line, but that requires shell access to the server. To be honest, I'm partial to your solution!
In any case, the missing capabilities (FALSE) for cairo, png, and jpeg is almost certainly your problem. Is it possible to build R from source again? In particular, after the ./configure step here, this same output should be presented. You can validate that the desired capabilities are present before moving on (to allow easier iteration). There are flags you can use with ./configure to ensure these are enabled.
For clarity, the yum-builddep R or apt-get build-dep r-base commands should have installed the necessary system requirements. So it would be good to make sure that the relevant command has been executed. I believe these capabilities default to TRUE if you have the relevant system dependencies.
EDIT: I am focused on the grDevices::png function here, but it is possible that X11 will matter too... I just know X11 is often not used for apps on Connect