I drop the neg flat onto the surface of the 8x10 tray of developer and push it down with my fingers and follow with the second neg in the same manner. I rock the tray for 15 seconds, shuffle the negs, repeat, for 10 min.

I think I might see the problem. Can you see a noticeable straight line in the negative that has the dark area?

If so this is caused by negatives sticking together and the bottom one receiving less development in some parts.
Sometimes when you are rocking the tray the negatives do not stack on on top of the other one perfectly, the part of the bottom negative that is covered by the top one exhaust the developer and has no replenishmet. The part that is not covered by the top negative is receiving constant replenishment and receives more development. So when you see the negative one part is underdeveloped and the other is correctly developed, and there is a very noticeable straight line, or corner.

The dark streaks as you correctly deduced is from uneven development. I would say it has to do with the way you are rocking the tray and shuffling the sheets. Try this, introduce your negs as you are doing. shuffle for 30 seconds, stack the negatives in the tray and leave it. dont rock it. After 30 seconds shuffle again, etc...etc..this my work better.