Hopper transfer keeps item order consistent 100% of the time as long as you don't leave the world.

The issue was discovered when using the redstone device in the images below.

The items are taken out of the shulker box and distributed down the first hopper line. When the first item reaches the end of the hopper line it is locked, while the hoppers underneath the initial line are unlocked. This effectively transfers one item into each dropper per rotation.

The droppers are then powered, spitting the items into a hopper line in front of them. One item goes into each hopper.

This is where the inconsistency arises.

If you've built this all without leaving the world, everything works as expected and item order is perfectly preserved. However, once you leave and re-enter the world the final hopper line no longer works as expected.

More images will show which items are switched. I did 3 tests, and color coded them.
The first image of a given color shows the starting item order before transfer. (Starting order)
The second image of that color shows the item order after transfer, before restarting the world. (This works perfectly)
The third image of that color shows the item order after transfer, after restarting the world. (This is broken)