First, for a studio, a CRI of ~80 for your LED lights is lousy. Sorry, but it can get too cheap.
Second, for this kind of application, I'd never go for LEDs. For beautiful colour rendering, halogen rules.
Now for a solution. Can it be (it's about baking, after all) that you have three-phase service?
If so, patterning your lights onto all three phases might solve it. That's then just a rewiring issue.