You don't need to sign up for all three cards. You already have 121k between UA and UR (assuming you get a card that lets you transfer the points). So you only need 79k more for J, if there's availability. Including spend, any combination of two of the Sapphire Preferred, Ink Bold/Plus, and UA Explorer will do.
I would sign up for the Sapphire or Ink + UA card. Meet the $2k spend on the UA card quickly, and you'll have 176k UA miles by October/November. Book business outgoing and coach returning, if you can find something available. Then when the Sapphire/Ink points post, see if there's still availability for business on the return. You'll pay a fee to change the cabin, but it'll be worth it.