Fixing a guest screen resolution in VirtualBox

So I tried this, and might work for you. Under the Machine menu, there is an option to auto-resize the guest OS's resolution to fit the monitor you are using. I got the resolution you did by enabling this option, manually resizing the window to get the resolution I wanted, then DISABLING auto-resize. Then, it's "stuck" there and I can resize the window, move it around, resolution doesn't change. Only problem was the taskbar. While you are doing the resize, might help to minimize it to get the exact resolution

For my setup, neither CustomVideoMode1 nor setvideomodehint nor MaxGuestResolution worked. So, I looked up

vboxmanage getextradata $YOUR_VM_NAME enumerate

and changed

Key: GUI/LastGuestSizeHint, Value: 800,600

to

Key: GUI/LastGuestSizeHint, Value: 1920,1080

with

vboxmanage setextradata $YOUR_VM_NAME GUI/LastGuestSizeHint 1920,1080

Try installing Guest Additions. It provides lots more features to the guest OS. From there, you can leverage the resolution you want and lock the screen in that position.