You should try a garlic cultivar requiring little "vernalization" (cold weather to the uninitiated). Thermadrone (French) and Lorz (Italian) do well even in mild Winters and Bogatyr (Russian) and all so called Siberians were selected to be planted in the Spring after the ground has thawed. Bogatyr can actually be planted and will do reasonably well even in hot Summer weather so it may be worth a try.
