I have just tried this and found that the inverter cable connectors were different. The 1211 display had a black lift up connector (the same as the adjacent fan) but the donor display had a white push in one similar to the iSight (see this photo from the 1150 guide and this one from the 1211 guide. I had to dismantle the top case and swap the actual LCDs. That worked, but takes quite a bit longer. see this guide. I could probably have swapped the inverter cable, but that seemed even more tricky as you have to dismantle the hinge and the cable is quite fragile. Doing the LCD swap also avoids the 3 into 2 antenna cables question, so is probably the best all round solution.
There is a potential problem with replacing screens in the 12" G4 1.33. If the existing screen is manufactured by ChiMei, then it seems that the video (LVDS) cable is sometimes specific to that screen and must be changed as well. See this Replacement LCD Not working Anthony
I have the exact same symptom (see this Why won't LCD from 12" G4 1G work in G4 1.33?). The Bookyard and iFixit both indicate that the LCDs are usable in all models. I am going to try the LVDS cable out of the donor machine, but that means a lot more dismantling first. I will post how I get on. Did you find a solution? Anthony