One of the biggest deterrents to running the weekly Khal mission, for me, is the lack of a multiplayer option. My opinion is that Warframe is just better with other players, and trying to do the Khal mission alone with all the extras can be extremely time consuming. I skip it most weeks because it's boring to do it alone.
So here's my thoughts on making the Khal mission exponentially better, with only minimum (if any) rebalancing needed: Clem!
Make the game mode cap at 2 players, instead of 1, and player 2 gets to be Clem. Canonically, it makes complete sense, and the dialog between them could be priceless.
Also, Ven'kra and Spragg should help you after being rescued, so there's a big incentive to fight them, even if only for a limited time, but that's a minor sidenote.