This is a pretty cool idea, but I'm still a noob on the tech side. If I wanted to do this but remove the CRT and and put an LCD or something in it's place, what do you think the major problems would be?
The biggest issue would be finding an LCD that nicely fit the original opening in the bezel, and doing the "carpentry" work necessary to make it look good. The iMacs had "15 inch" displays, but that was the diagonal measurement of the tube, some of which is covered up by the plastic around the edges. The hole itself is around 14" diagonal (I don't have an iMac anymore to measure exactly), and even though the iMac used "flat" CRTs the edges are slightly bowed, rather than *flat* like an LCD.
Thus to make it look original-equipment you'd have to find a 13 or 14 inch LCD monitor (14 inches wasn't *terribly* uncommon as an entry level size around 2003 or so, but you'll have to look for it), carefully skin it and construct mountings to fit it into a gutted iMac case, and then see if you can cook up some sort of curved (and smoked?) piece of glass or plastic to put in front of it to preserve the "stock" look.
(If you don't care about it looking *exactly* stock I imagine a black matting adapting from the original edges down to a slightly smaller LCD would do.)
If you're looking to preserve the original iMac motherboard then the most straightforward thing to do would probably be to make the wiring harness from an "ATX conversion", remove the original power supply and analog parts, and sub a less dangerous ATX supply into the space freed by removing the CRT.