I've done 3, and all of them have been different based on the cabinet. I'll give a brief description of all 3.
Taito cabinet: The cabinet is made to where you can cut a piece of plywood as a monitor mount and have it slide in and out of the cabinet on rails. I cut a piece of plywood to size, then marked where the bottom edge of the tube needed to be to match the bezel. I also measured and placed the tube bolt holes onto the board. Then laid the tube on the board and traced it. I had to cut out a chunk at the bottom to allow the chassis to slide through too. I left the chassis mounted to the plastic bottom piece, which I then secured to the plywood board with screws. It was a quick and easy way to mount the chassis securely.
Narc Cabinet: This cabinet is modular, and the top monitor compartment sits flat. All I had to do was decase the monitor, slide it through the hole, and let the chassis (with plastic mount intact) sit on the bottom panel of the monitor compartment. Then I cut pieces of 1x2 pine to fit diagonally in the corners to give places to screw in the tube bolts. This was by far the easiest of the three since the bolts aren't really supporting the entire weight of the monitor.
Pacman cocktail: I reused the existing monitor mounting frame for this one. I also realized the cardboard/foil 'cage' around the monitor acts as a perfect chassis support. Thus, I zip tied the cage to the mounting tabs of the tube. Due to the flat face of the pc monitor, I had to adjust the mounting height to bring the tube face up to bezel height. I traced the tube again onto plywood, and cut a top and bottom piece that bolted to the cabinet monitor frame. Note: the plywood was doubled up to bring it up the proper 1.5" in height. Then I dropped in the monitor and screwed it to the plywood braces. This one was an incredibly tight fit, especially with the cage intact. I had to dent it in alot to get it to fit.
In closing, you will have to get creative to get the monitor in. Don't get too creative though, stick to KISS (Keep it simple, stupid). Jump in the deep end and just go for it, or else you'll spend way too much time overthinking, and not accomplishing anything. I let this hold up my Taito project for over a year!