Oh, and I decided to do it anyway. Djinn is wrong.
The highest AP build is
if you buy boots, and we don't count the active on Spellbinder.
If you DO count the active on Spellbinder, then swap one of the Luden's for it. (You did say no dupes, but I assume you meant no dupes if it means hurting the gold efficiency of the build, which buying two Luden's doesn't since it's already 100% efficient even without the passive)
Archangel's and Transcendence together actually make the bonus from mana and CDR on a second Luden's beat the bonus from a fully stacked Mejai's.
You do need Transcendence and Manaflow band. Bring the cooldown shard, NOT the first adaptive damage one. Transcendence makes it give you more AP than the adaptive one.
Ah, and since you say you absolutely need Cosmic Insight, also bring Biscuit Delivery for the extra 160 mana, which will give a little more AP but not as much as Eyeball, Ghost Poro, or Zombie Ward would.
Honestly I don't get why people don't just test these things out for themselves.