If you don't have CO2, maybe get slightly smaller bottles too so you can fill right up to the top? Judges will note a high fill, but it shouldn't affect your score and the lack of headspace will help maintain carbonation after transfer and eliminate oxygen.
The bottles have to be 10oz, so 11.2oz bottles that many breweries use now would work. Guinness draft bottles have shrink wrapped labels that you can CUT off, very easy.