I may be completely off base on this: In Eve, under Display and Graphics, set fixed window. Three options down under "Display Adapter", I can set which output port on my graphics card will have Eve. My graphics card has two output ports (for two monitors). Once I set that, I sign in on my first monitor but the game launches on the second monitor full screen.
Congrats on your good start! I have followed but FYI I rarely watch streams just cuz of my chokingly limited data allowance...except when I sometimes splurge and spend it to watch Mr. Splunk play a game I'm interested in. Did watch your Grand Opening VOD for a few minutes, though...very professional!