Well, with the remaining trust available at this point you might just as well use something cryptographically secure, like encrypted ones, twos, or simple HMACs of the block number.
A too-simple scheme is likely to be detected (and bypassed!) by the firmware a nearly no time.
though I wouldn't expect this exact command sequence to work unless tee's buffer size divides /dev/DEVICE's capacity and tee errors out writing past the end of /dev/DEVICE before writing to stdout.
Try http://xpra.org/ - that's a "gnu screen" for X11, but bandwidth-optimized, can also relay USB, audio, ...
Just to give you an idea: I used it for forwarding a Firefox window across an UMTS connection when sitting in a train. (Long story: 32bit Java required to remote desktop into a client's environment across the Atlantic, ugh.)
I have tried xpra, and it was my go-to option until I tried NoMachine. I did try just forwarding windows, Firefox it was too, but there was some(times) frustrating delays.
I may re-visit, however, as the delays could have been network/environment issues rather than the technology.