I think what you are seeking is how to utilize X as it was originally written.... A lost art my friend.
For those unaware, X does not work like Windows systems. Any X based application issues commands as a X client, that is sent to a X server. When you are on your local machine, these machines are the same, and the protocol is hidden my going across localhost. On Windows based machines, program write by callings APIs in the OS that ALWAYS write to the local machine. The result is, that Linux does not require video on the local box, just the X client. You can, unlike a Windows box, have your programs write directly to your remote connection! If your X client is connected to your X server over say SSH, via port 6000 (fisrt screen, 6001 for second monitor, etc), your Linux desktop can display on your local X server (for Windows desktop use MobaXterm), while running at AWS.
Enjoy
Kevin Fries