Looks like SPICE could do it, found this comment on Wikipedia:
Xspice
The X.Org Server driver for the QXL framebuffer device includes a wrapper script[11] which makes it possible to launch an Xorg server whose display is exported via the SPICE protocol. This enables use of SPICE in a remote desktop environment, without requiring QEMU/KVM virtualization.
How about making the LM box auto logon upon reboot. This will ensure desktop:0 is always running, then when you X2Go into it, you'll be a secondary connection, and your should should come from your desired location.
I suppose one could.
For the now, I'm using the dying monitor to sign in with. it'll work long enough to sign in before the video goes out on it.