There's sooo many ways to go about doing this it's hard to tell any one person just exactly how to go about it.
Theoretically you could get the monitor "kit" you first posted about and swap the tube and parts into your existing frame, you will probably have to mount the chassis a bit differently.
Or you could go with something like this:
http://www.happcontrols.com/monitors/490727vp2.htmEither of those ways you will need an inverter adapter of sorts like from Mikes Arcade.
http://www.mikesarcade.com/cgi-bin/store.pl?sku=NININVAMPOf course he does also carry a ready to go drop in, plug and play monitor, bit pricey, but an option.
http://www.mikesarcade.com/cgi-bin/store.pl?sku=MONITORNPeople tend to have varied opinions on monitor brands and such, but basically if you buy an off the shelf 19" CGA monitor remember that you will need the adapter and you will probably also have to do some minor wiring harness changes in order to connect it up to your Nintendo cabinet. (video signal connectors may be different) And be sure that it has either a universal or vertical mounting frame.
One other thing to note is that the Sanyo runs off 100V ...... so the power "outlet" that is in the bottom of that cab in which your monitor is plugged into now is only 100v AC.
A typical 120v monitor will run on this, but it may be a bit flakey. So you may or may not have to re-route power to the new monitor.
Just out of curiosity ...... what's wrong with the monitor you have now?