While not the optimal solution, I'd go ahead and store it full with stabilizer added. I've used 2 year old gas that had no stabilizer added and even though there was an obvious loss of performance, it still ran. Just be sure to spray carb cleaner in the carb every once in a while to keep any residue from building up and I think you'll be OK.

The thing about stabilizer is this; you must have it in the gas that you use so it's already in the carb and every orifice before you store. Just putting it in the gas tank before storage does nothing but preserve the fuel in the tank - the gas in the carb is left to turn to varnish and cause a carb overhaul later. If you do this right, there will be no need to get it out and run it during the year or to waste the fuel in the tank when you start using it again. In addition to the stabilizer, add a heavy dose of Marvel Mystery Oil to the gas, maybe 2 oz in the mower tank, and run some of that through. Also use MMO in the cylinder. Change the engine oil and run the engine only for 30 seconds or so. Clean all the grass build-up from under the deck. Any bare metal under the deck should be coated with a waxy corrosion inhibitor like Boeshield T9. When started after storage, the engine may smoke a little for a minute but nothing special has to be done - just use it. BTW, continue using the stabilzer and 1 oz/1 gal MMO - the mower will love you for it!