I usually don't answer my own question, but in this case I have to I guess.
I am running Minecraft pre-release 12w36a and I can confirm that you can cure infected villagers spawned from dungeon zombie spawners in survival mode.
I had a zombie spawner underneath my base that I never destroyed, I am glad I kept it. I set up a small killing device for killing the unwanted zombies, and waited for a infected villager. In my case it spawned one every 30 zombies or so.
When I got one I used a splash potion of weakness (water bottle + fermented spider eye + gunpowder). As soon as I threw it I got my golden apple in my hand, and just right-clicked the villager. At this point he started shaking.
While he was shaking, I waited around. About 5 minutes later he turned into a normal villager.
At this point I wanted to know if he would despawn, so I went exploring in my world, slept for a few days, and went to the nether a few times. When I came back he was still standing there, which was great.
I do not know if this will stay in the game. I will update the game once in a while to see if it still works in the snapshots.
For now I will work on setting up my village, I am glad I don't have to build the 1000+ block railway anymore.
I can confirm this works in 1.4.2, see the video in the question for more details.
Your villagers need a village to breed. A wooden door will only count as a house if one side of it is "outside", which is to say has nothing but air blocks above some block within 5 meters.
So you could fix this be building a chimney though the ocean above every door.
Best Answer
If you're playing multiplayer let your friend right click on the villager when he is in the trading menu right click the villager with the name tag.