Unfortunately with USDA you cannot own another home in habitable condition in the same commuting area as you would be buying your new home, which is something you seem to realize since you are asking about that exception - so you would need to purchase the new home simultaneously with the sale of your home. My information is based on a conversation I had with a USDA representative in Nevada about someone who was moving 60 miles and selling their old home, which I thought was far enough away, but apparently it was pretty common commuting distance in the middle of the desert and so USDA required them to wait in order to purchase with their financing.
Can your renters buy the home earlier than December? If there is a new construction home that will be complete in ~4 months, you could make an offer now and time it with the sale of your current home.
If the home you are renting is not within commuting distance, then you can own that one home only and should be able to purchase with USDA financing.