I started using a soilless mix about a year ago and I'm still dialing things in so it would be difficult to draw any conclusions beyond the meter readings I took, but all is well in the mirror space. I'm good at hydro and have a ton of grows in that space so if I went back to hydro I might be able to tell if there was an obvious benefit to using mirrors. Once I feel confident I'm getting the most out of the plants with soilless I'll go back to hydro. Probably won't be any time soon but I'll update if/when it happens.
Good news is there are no negatives to using mirrors. Plants seem to like it, no hot spots or burn issues. I ended up putting mylar on the doors covering the last 1/3 of the wall surface. I'm pretty happy with it. I wouldn't consider going back to white.