Adding C-Channel without routing

I am building a desk from a 8' butcher block and am running into an issue with sagging/bowing. There's currently no weight applied, and I added central legs. There's about 1/8th of an inch of deflection in the center. The top has 10 coats of wipe on poly, and the bottom 5, which is why I imagine I'm having this issue.

I'd like to add a C Channel across the bottom, but don't want to mill the slot for it, rather mount it upside down. Would this cause any issues? I'm thinking a 7' piece should do.

Pic for reference.