In the areas I hunt (western middle and west TN), I would say the gobbling peaks around April 10-15 in a normal year (normal temps, normal spring green-up, etc), but last year peak gobbling in my neck of the woods was way early as was most things, with it peaking sometime around juvenile weekend, or possibly earlier.
Where I have hunted, Giles, Lincoln, and Wayne, and also North AL. On a normal year with average temps and average green ups it is always from about April 23rd to May 5th. This is when most of the hens have gone to setting. That last week of the season, or about May 5-15, They gobble pretty good but it seems they are harder to call up. It is like they just gobble to gobble, and they are in bachelor groups.
You have to understand that this is mostly private land, and they don't get near as call shy has public birds. I bet public birds the best gobbling is the first week or so before they all get spooked up.