Hi Digby, welcome to Cruise-Chat. Congratulations on a fantastic voyage. By all indications, you should be ok in the first part of September. August would be a safer bet, but you should be ok in September.
This site might help you some. If your suitcases are no more than 12" high, when you lay them flat, you will have no problems fitting them under your beds. If you have a twin size bed, or a queen size bed at home, you can try fitting them under your bed at home to make sure. If you have waterproof jackets with zip-in linings, that would be good to bring. Pack some clothing that you can layer. Are you cruising around the world, or comibining tours? It sounds like a fabulous adventure. Best wishes and once again, welcome aboard!