RDP is still 10 times quicker than anything linux has to offer in this area
Except for RDP, of course. Linux offers RDP, and this protocol is obviously not 10 times quicker than itself
Pardon my pedantic attempt at levity. I haven't actually used RDP in Linux for ages, so I don't know how current implementations compare to those used in modern Windows, but I glanced on Wikipedia and found something you might find interesting: "In 2009, rdesktop was forked as FreeRDP, a new project aiming at modularizing the code, addressing various issues, and implementing new features. FreeRDP comes with its own command-line-client xfreerdp, which supports Seamless Windows in RDP6." Seamless windows is the thing you're looking for, so maybe give FreeRDP a try.