Out of my TAP research, I've created a tool that can generate a sequence of items, and prints out statistics of the item generation. Attached is an archive of C source code and a Windows 64-bit build. It's a portable command line program, and will give you directions on its use.
Explains exactly what's happening and why the items are coming almost as a list : Nega field has a 1/(sumOfAllItemsWeights) = ~1/2000 chance of appearing at the beginning, just slightly decreases to 1/1750, 1/1500 etc... then 1/20 all to way to 1/4 before being the last item in the bag. That's the price of having a weight of 1 versus many other items with a weight of 250, 50, 100 etc. Same for a lot of the late items except that probability is multiplied by 3 or 5, which is still very low. Funny that right mov field and left mov field have drastically different weights (50 vs 3) Thanks for the findings!