Have you considered a Mister FPGA unit?
https://en.wikipedia.org/wiki/MiSTerhttps://ultimatemister.com/https://misteraddons.com/The platform is becoming much more mature and is popular for emulation of older systems and games. They are constantly adding new cores or improving older ones. The emulation is very high quality.
The system is modular, so you can add stuff that you think you'll need. A common setup would include the required DE-10 nano, a USB board and an analog IO board (VGA/D15 out) that gives direct native 15Khz or whatever is required. No special video card required. Even does component video out, so you can use that old CRT TV in the basement. Just edit a few settings in the config file. With the HDMI already included on the DE-10, you can choose whatever display is most convenient and you can swap configs with hotkeys.
A setup like above would cost you a few hundred dollars, probably a little more than those TVs. Depends on what you want, bundles are available or you can assemble and setup yourself. Links are just suggestions, you can get stuff on other online marketplaces. There are some nice cases available too.
There are stand-alone two-player control panels available for arcade games, which allow you to sit at a lounge. Combine that with some controllers for consoles, and you might not even need a cab.