In order to not change the reach or rise while achieving a flatbar hand position (it sounds like this is a goal of yours), you would likely have to go with either a BMX bar or apehanger bar to meet your goal.

BMX bars are avalable from about 6"-10" rise and you can angle them backwards. Many have 22.2mm clamp area so you'll need a shim to shim it out to 25.4, I'm guessing this without knowing current bike specs. Ape hangers are generally 18-24" rise.

They may have a fair amount of sweep so it won't be totally flat bar position, but BMX bars get pretty close.

Here are some long apehangers on a recumbent: