Hello, I have searched everywhere for this answer and it seems the interent does not have an answer

So i come to the open source forums where I am hoping somone will have the answer.
So currently i have a Canon 600D connected to a trinocular Leica microscope (not connected through the eye piece), I get a beautiful crisp picture good enough for microscopy publication and work wonderful for in class practicals for students. Also my researchers are now documenting all of their microscope work on this setup.
I am using EOS Utility on my PC and then from my PC using a HD cable to a huge 70 inch Sony LED 1080p TV. It all looks great.
But during "Live video mode" the picture is fairy small and only takes up half the TV. Students up the back of the class have to come down the front so they can see properly even on this big screen. I can take a picture or a video recording and play it back on "Full Screen" and everything is big and covers the entire screen, but i like to do this live instead to show the students how to use a microscope at the same time.
I have looked for a "Live View mode" full screen button/menu but i can find nothing. How come this is not a feature? I a have plenty of rendering/processing power on my computer.
I love the easy use of EOS utility for my teachers and students.
I have recently been reading that the Canon 600D is a crop sensor and now realise why what i saw down the microscope was not what i got on the screen, in fact only one half to a third of whjat i could see down the microscope was displayed on the screen. So i stopped looking down the microscope and just learnt to use it off the screen.
I am looking at a Canon 6D because of its price tag and it has a "full frame CMOS sensor" which i presume will let me project to the screen what i see in the microscope or at least a lot more.
The big question is will this also increase the size of the display on the EOS Live view mode screen? If not has anyone achieved this?
I also noticed the "Zoom" box can be removed by some after market programs, i presume there is no easy fix to get rid of this within EOS utility? Its annoying not being able to get rid of it.
Thank you in advance, I should warn i am a complete novice at this and just hope somone here can help me out