You're already at the 5/24 limit? Makes it harder.
Go to awardhacker and see who flies there and what points you'll need.
AA might work. Get the Barclay Aviator (60k miles for $90+1st purchase) and then the Citi card for another 60k ($3000 spend). It looks that'll get you Business (75k miles) or First (120k miles), one way.
Then consider an AmEx MR card and an AmEx SPG card and transfer those to Kris or Aeroplan. That'll get you business class for 75k, one way.
Oh, I should add that awards seats, especially above economy fare, go quickly. As in, 10 months ahead of time. Get the business seats you want first. You can always return your economy award seat for a fee if/when the business award seats open up a week before the flight leaves.