Test update: Everything works as it should.
Asked about Tower first-brought none, one and two, only advanced with 2 horns in inventory, Forsaken second, brought in none, one, two and three, only advanced with 3 salts in inventory.
Switched research order, same results on same tests. Both avenues of research were available regardless of order.
Amy issues are probably being caused by the wrong item being brought while a certain research is happening. To clarify in game, you could edit Rar'azar's text to say which research he is still working on, even though Journal makes it quite clear...