Report them to both the IRS and to public stock markets.
Yes, it will reduce your publicly reported earnings, as it should. Smart investors & analysts will quickly learn to account for that. In fact they already do with constructs that are bogus from an actg point of view, like EBITDA, but useful from an investing POV.
Indeed, it will be very useful for investors to see that Company X and Company Y both report $100 of earnings, but Co_Y is reporting that number after taking $50 in loss carry-forwards.
Again, paying on the greater of SEC-reported earnings or tax-filing earnings hurts only companies that are trying to scam the system and their investors. It helps everyone else, including you and me.
You want the capital market benefits of reporting big profits? Fine, pay the commensurate taxes. Letting them have it both ways is literally telling the thieves to have a nice day as they walk out the front door with the contents of your family safe in their bags and your electronics on their carts.