May depend on your outdoor temps, and great disparity in temps can cause stress, which can affect overall health.I assumed that around 3-4 weeks they'd be large enough and well feathered enough to move outdoors but it sounds like from what you're telling me i need to "wean them into it" so to speak?
I don't know about lamps causing 'eye problems'...but lamps can be dangerous and, IMO, best for them to experience day and night cycles.I'll be going with the Ecoglow 600 heat plate I mentioned earlier; I had concerns about lamps causing eye problems when on 24/7 which led me to find this thread.
Hopefully you are doing some 'gosling' searches and reading.