The templars weren't in complete agreement with the church at this time, as the French King (check my history please) was trying to turn the pope against them. Therefore, it makes perfect sense that Da Vinci would be among their ranks.
Dude, i tried finding out some info for you on the Fallout 3 bethesda forums and they dont know shit! The only thing i found was this:
"Like heaps of you I was trapped doing the waters of life quest (Pre and Post patch). My first run through I cleared out the memorial before going into vault 112. To get around the problem I didn’t enter the memorial until I was instructed to. Which solved all the freezes? (Why?....Who knows)I lost about 30 hours of game play, ohh well...but at least I can now play on. I recommend saving often in different slots to help with future freezes. Hope this helps."
I'm not to sure if this will help you, but i hope you can sort something out because it takes the piss.