Seriously this is a topic that belongs on Applefritter ... nevertheless, I think Tom Lee would agree with me that cutting up these old boxes rather than restoring them is sad unless they are already damaged beyond restoration. However, that said I think MacMan is correct in that you need to fit the design of the case which took into account the shape of the monitor. This takes the "plastic insert" approach and proves my point:
http://apptree.net/macsex.htm
It just looks wrong as does this:
http://ww1.tiki.ne.jp/~jm4vnq/classic/index.html
A classic example of this is the PowerMac 5200 series. Apple designed it for the Sony Trinitron monitor like the Color Classic and LC 520 series. But at the last minute, they switched to a regular curved tube and the result is just awful looking.
If I were going to put an LCD in a case, I'd try to find a curved glass or plastic substitute. I might even cut the front off an actual dead CRT.
Whatever you do, please don't destroy a 128K, 512K for a Mod these are the rarest of cases.
If you're going to mess with the overall case design, I'd rather see these kinds of mods anyway as it saves the case and the guts:
http://www.bernardbelanger.com/computing/setv/index.html
http://www.bernardbelanger.com/computing/cube/index.html
http://www.bernardbelanger.com/computing/proto/index.html