Might also want to mix in some vitamins, minerals, other essential nutrients that may be missing if you dilute them by 2/3 with corn. A way to increase protein back up to 16 may also help. I personally would use corn as a treat or something to finish off meat birds with if you plan on keeping the layers for more than a few years. Decreased minerals, protein, and other stuff can reduce production since it's not there to make eggs from. Plus, don't let the birds get too fat in the winter or they can build up fat deposits on their reproductive tract which can increase the risk of prolapse in the spring if they stop and start laying again.
However, do as you wish with the feed as 10 people will have 14 ideas and way that are tried and true to feed their birds. There are flocks out there that only get cracked corn as feed and otherwise have to fend for themselves, and flocks who get premium organic layer at a 20% protein content with extra minerals for feather conditioning.
If you could run half your flock on your mix, and half on just layer, and compare them at the end of winter, you'll be able to see which regimen works best for you.