I said it is hard to make well formatted.
But you are right, construction 6 should be in fact researched before alteration 5 because you want the bracelets. So let's try this again, assuming a decent water gem income: alteration 3 -> construction 4 -> enchantment 5 -> construction 6 -> more alteration & enchantment. Make quick dips into other schools when you have enough research points to get the first two or three levels in one turn.