I've solved this by buying FastX from StarNet. I run a server on Linux and display my X programs on my desktop at work. When I get home, where I run the client on my home desktop, I can connect to the same server and disconnect my work clients and reconnect them to my home machine. It's the perfect solution for me.
Because that's what mosh is designed for. Graphical programs are off-topic.
By the way, we have used xpra ("screen for X") with success in the past: https://www.xpra.org/