Without actually trying this....(keep this in mind...this post is 100% theoretical)....I would think you could rig both the front and the back brake levers to be on the right handlebar so your right hand could work both of them.
You might have to get creative to make them both fit. But as far as functioning you can easily move the left hand lever to the right side of the bar. It'll work just fine. But if you flip it over there is a chance the oil reservoir for the hydraulics could leak so you'll have to make sure it's tight. Then I'd think you could zip tie the front and back levers together so you only have to pull on one.
Again...this is theoretical. You've have to screw with it in person and see what did and din't fit. Plus you've have to figure out how to make your gear shifters work among all that.
I don't know if there is a hydraulic split that would let you have 1 lever work both brake lines. But that would make it easy.
Like I said...you'd probably have to get creative. But I bet you could rig it so both levers were on one side and worked together.
There are only about 100 things that could go wrong. So it would take a lot of experimenting to get it working well.
Or...just a second right hand lever and just move the front brake cable over to that one. That eliminates the upside down reservoir problem but doesn't resolve the "both levers are not designed to fit together on the same side" problem.