Cheap alternative is to pack the bottom up to 18 inches of clay, rather than just a few inches worth, if clay resources is available for such task. The clay that you're using may contain higher content of sand, or loamy-sand. Thicker compact layer will slow down the leeching even more, but will not fully stop the saturation and leeching process for your particular clay content. I can't tell, since I don't don't have it in front of me. Maybe a geological location of your site could provide a better oversight, since I can use the USGS Soil Survey data to pull up your soil content. During hot days, the evaporation will be at a much higher rate than the percolation/leeching.
If you have the budget to go with a liner, even better. The cost will climb real fast for the liner to be covered on a 2 acres site.
