Looks like a pretty ingenious setup you've got there. It's not ideal, but it's pretty good considering you weren't planning on getting a turkey egg to incubate.
I'm sorry I don't have time to read the whole thread so forgive me if I'm repeating what anyone else has said...
Lockdown and hatching, you will hear Dexter cheep before you see him pip. Then he will make a small hole, or pip, in the shell. Then he will rest, for hours, he should still peep periodically but it's ok if there is no more progress for awhile.
Humidity... the wet sponge is good, but watch it once it pips, it should make a hole or crack in the shell, this lets the moisture out and the fresh air in. In an incubator the rule is DON'T OPEN THE LID!!! But you do not have a normal situation. I would keep an ear and an eye on him. Once he has broken a hole in the shell watch the inner membrane which should be clear. When it starts to dry out it will turn white, like rice paper, which is nearly impossible for Dexter to get through. If it starts to get dry, or even if you are just worried it is too dry, wrap the egg in a wet paper towel. If you just lay the paper towel lightly over the egg, air should still be able to flow through the channels created by the wrinkles.
Once Dexter starts to zip, I would keep wetting the paper towel and lay it over the open part, keeping he open space wet. You want to keep the membrane wet enough that the chick can move it and work his way around in there without making a puddle he can drown in.
I'll be back later to see how you're doing and what questions you have.
