Here's the Xbox machine I had. I still have the cabinet, just with a PC now. I never had any overheating issues. The Xbox case was removed for no particular reason.



Here's the padhacking birds nest I had. Later on I did the smart thing and built a proper Xbox > JAMMA converter by soldering all the stuff to a JAMMA fingerboard and stuffing it all in a box. You'll certainly want to do it this way if you plan on using the original Neo Geo hardware again. Note the subwoofer hanging under the control panel... by the way, the Ultimarc stuff will do video without problem, but you may need to build an amplifier for sound; the Xbox can't drive those speakers by itself. I gutted some PC speakers and connected the amplifier to the cabinet speakers originally, but for my Xbox > JAMMA converter I just made my own.
Here is the back of my MVS, with PC stuff secured to a board.

This is all you get with an MVS *-25, a small panel at the bottom for working with the power electronics. There is a very small removable panel at the top that lets you
look at the monitor, but you can't do anything to it. The only way to service the monitor is to remove the glass on the front of the cabinet and remove the monitor completely. Also, note that the large power supply at the bottom is not connected to anything, the cabinet was actually using the smaller switching supply you see on the left, with mains passing through the old supply. (ignore the PC power supply)
To open a Neo Geo you have to open the coin door, stick your arm up the right and left sides of the top of the control panel and unhook two latches. The panel will then swing down like a door, and you can access the board, change games, fiddle with the monitor's remote board, etc. Here's mine with a modified JPAC connecting a PC-

Note the latches at the top.
And here's some control panel images from
Payment_Due's Neo Geo restoration thread.

As you can see, you can't just use a piece of rectangular metal or wood. You may be able to get another MVS panel and modify it if you want to keep the original around.
That's all I can think of for now...