https://www.schneier.com/blog/archives/2014/03/ragemaster_ns...
There's no direct solution to the subverted monitor problem that I'm aware of. You basically get them from random places under different names or from people unlikely to be spies then use I/O protection both ways. Same with most hardware you can't produce yourself. There's potential to market something here where the monitor is immune to code injection, does I/O filtering, can't store anything, and does these with visually-inspectable chips & board. Add TEMPEST shielding while you're at it since that's an existing market that will drop lots of cash on improving security. See EMCON's products for examples.
EDIT: Forgot to mention that spectrum analysis is often used to try to catch radio emissions. There's techniques to tell if monitor sends out stranger than usual signals. That's just kind of limited and doesn't help if it's black bag job where person can show up twice (eg maintenance person).