I am trialing multiplicity as an option for my work/home setup to switch between my gaming rig (primary) and my work laptop(secondary). Hard to find a hardware solution that supports 1440p 144hz G-Sync DisplayPort that doesn't cost a kidney.
I found this thread, as I ran into the same problem. My current workaround is a usb-c dock with HDMI also connected to my monitor. This allows the laptop to provide video to my monitor, at 1440p resolution, without it being viewed by the monitor thus keeping the laptop video alive even with the lid shut.
I'm also using this dock for my USB busy light since I don't need that on my gaming rig. Another benefit of the dock is the network card. I have the ethernet NIC from it connected to my 2nd NIC in my gaming rig, set up as a private crossover just for multiplicity. Near zero latency, full gigabit bandwidth, and it doesn't interfere with my company VPN connected via wifi.
Only feature I would like is the ability to share all USB devices connected to the primary with the secondary. I use my webcam on both devices, usually handling switching with an A/B usb switch. If I can find a solution for this, I would gladly purchase the full version. Until then I'll manage with changing inputs on my monitor and clicking the button on my usb switch.
If you're tech-savvy you may also want to take a peek at Apache Guacamole™
I use it for all of my VMs and misc headless machines. Not sure how well it works with laptops with the lids closed, but may be worth investigating.