Thanks for the photos bro.
Here is a Google Search of this site with 38 results for the words: gear tooth stress
Please read through at least the first two pages of links. Note that some discussions are more than one webpage long and you need to click the 2 to get to page 2 of the discussion.
See how they don't model a complete 360 degree piece of the gear, but maybe only a 30 degree slice. Pay attention to the size of the elements, see how small they are at the contact point. This is where you need to go to get a better agreement between your model and the hand calculation.