Nice idea!
Those beige era Macs were amazingly solid and well engineered bits of kit compared to the majority of their PC counterparts! I was a former Performa 6200 owner before I made the jump to the (awesome) blue and white G3 tower...
Not much I can really say about the case mod idea but I would think the mac mini style build would fit without much problem.
Anyway, getting (slowly) to the point, several years ago I tried fitting a 15" LCD screen into an empty iMac case. (original Bondi Blue).
I had a 15" (4:3 ratio) LCD display going spare so after a bit of cutting and bodging on the inside of the iMacs screen bezel I got the LCD to fit surprisingly well, except for 1 issue.... the curved front/face of the iMacs bezel which was designed to fit around a non-flat CRT display.
At the left and right edges of the screen it was a nice tight fit between the screen and the bezel but towards the centre of the display/bezel there was a gap of about 10-15mm (from what I recall). It basically looked a bit messy and I couldn't think of a neat way to fill the gap with the tools/materials available to me at the time.
This image kind of illustrates the the non-flat display:
http://www.mactechnology.co.uk/ekmp...able-drawer-loading-cd-drive-complete-5-p.jpg
I suspect you would have a similar issue with your old Apple display as I think most CRT's had slightly curved glass. Maybe you got lucky though and its a Trinitron style display with much flatter screen/bezel?
What actually led to me abandoning my mod was the fact my LCD only had a resolution of 1024 x 760. To get a high res 15" screen at the time was expensive, especially just for a 'fun project'.
At least LCD's are a hell of a lot cheaper nowadays so it might still be worth you investigating whats out there and seeing if there is a size, ratio and resolution that would work well with your old display case.
Have fun!