Hi, welcome to BYC!
Well, there is a back up of eggs that have already started forming.. isn't there?
They are still pullets. The terms hen, rooster, and cock are reserved for bird over 1 year old. Just as technical info in case you didn't know that. I know at my house we still use those terms sometimes even though we know it isn't accurate.
Also the 21st was the shortest day of the year and we are heading back into longer days.
In MY experience, the shortened days of winter may SLOW down the current years pullets... but NOT stop them completely. I'm at the California/Oregon border and DON'T provide extra light. In Louisiana you should be getting more light than me. Some of my girls who molted have already returned to lay!
There are MANY things that effect laying. The move may have upset them a little as they are creatures of habit and anything out of the ordinary CAN have a profound effect. But should NOT have taken 6 weeks. Maybe there was a late night predator visit. And nutrition is KEY! What are you feeding including treats and supplements?
Also the light may have had more of an effect than I'm used to since they had it for a while and then it SUDDENLY stopped. That's a change in routine and light hours plus a move all on the same day!
One way to combat the winter lull in production is by adding a couple pullets every spring. Even if you provide extra light for your ladies in their second year (winter season), they WILL still molt.. at which time they won't lay eggs for at least a couple months. Alternatively, you can stock pile eggs next year. Unwashed eggs in my fridge have lasted more than 6 months in the past and still been equally as good as store bought eggs. Plus there are methods of freezing or dehydrating if needed.
One final suggestion.. having different breeds also helps to combat everybody molting at the same time, though there will be individual differences still among the same breed.
Turken should not lay daily as they are a dual purpose (dp) breed. Many new layers will lay very prolifically when they first start and then have to take a short break. Had some DP birds lay 21 days in row, 1 day off, another 21 in a row, 1 day off, 15 or so and then a couple weeks off. That was when I lived in Southern Ca. Chickens are whack and they don't care about "rules".
Hope this helps.