Hehe.. damn you, Level! Don't be so religious. Ok, let's take Star Wars '83 as en example. The Amplifone xy-monitor is a display device for vector games, meaning that several other vector games could be displayed on this monitor. However, since the Star War's hardware is dependant on that particular monitor (there aren't many monitors this game can use), I would call it original for the game.
In the case of Galaxian 3, you could, if you wanted, crunch the whole thing into a 2x CRT monitor cabinet, like the cabinet for Darius by Taito, the sound can be mixed into two channels, and the game could be played with analog joysticks in a much smaller environment. What makes G3 such a large enterprise is its cinema theme with projectors and multi-channel audio. However, nothing of that is original for the game. You can use any projector, any audio-system, that you please for the G3.
As for any lag in projectors, well, consider the game's property then. It is 60Hz, in 60 fps. The lag you mention will never be relevant within these frequencies.
I'm curious about the artifacting you mention. Please, explain more?
Picture size: Ok, this could be a problem. So before selecting a projector (have you ever been shopping for a projector?) you need to consider the picture size VS throw distance. This is always thoroughly described in the specifications in every handbook.
Have you ever compared an older CRT projector with a DLP, or LCD from 2010+?
To restore a CRT projector to better shape, it is required that you replace certain capacitors that have been close to hot spots, as well as all three R, G, B electron guns. This is not exactly cheap.
"I would trust the Namco PSU's in there now with the caps of that era a lot more than crappy china built PSU from today."
- good point. 1999-2007 was the "bad-caps" era. But remember that every capacitor, chinese or japanese, has got its estimated life time. After that it's a gamble to leave it in the equipment. It could damage your game.
Btw, Level, have you made a cap-swap in your Star Wars yet?