You are right....my wild turkey eggs had VERY strong membranes AND, for that matter, the shells themselves were much thicker and stronger than  regular eggs.  However, I can tell you that all 6 of mine came out of their shell without any help whatsoever.  I candled mine almost daily (just couldn't help myself! ha) but I still can't help much with trying to date yours based on your description.  You also might be interested to know that I believe mine had not been incubated at all...that the hen was still in the process of laying and not yet setting.....I say that with confidence for a few reasons.  For one, there were only 7 eggs in the nest (only one was broken by the mower, but it didn't run completely over the nest...just close enough to get the hen when she took off the wrong direction (sadly).  Also, those eggs stayed there for almost a week before I got my incubator and set them.....so obviously they hadn't been previously started incubating.  Anyway, the reason this might be important to you is that the time it took....from the day they were set until hatching began...was 26 days...including the day I sat them which most people don't count.  Everything you read about turkeys says 28 days, so at 25-26 it was a little sooner than expected.
You'll definately get lots of debate over whether you should try this or not....but I can honestly say that on BYC the people were all extremely nice, even if they felt I should have left the eggs alone to rot.  I basically told everyone that whether they agreed or not, it was the right thing in my mind AND it is done so no need to fight about it...might as well try to help me get it right...and they have.  People here have been incredibly helpful and kind.  Turns out one of my chicks is badly deformed and going to have to be culled, something that broke my heart and has been next to impossible for me to bring myself to do, but the people here have been more supportive than you can imagine.  Anyway, point is, don't worry about the debate and contrary opinions...ask for help here and you'll get lots of it.  btw, look in the turkey section and you'll see some photos of my chicks if you want to know what yours will look like.  VERY CUTE!