So is waiting for your day to roll over.
Also max amount of turnips you can store is 10 x 12 --> x6 pages per storage letter --> x3 storage letters +160 for regular inventory space for a maximum amount of 2320. Dunno if you can just throw them on the ground, if you can, you still have a gross looking town/or house that you have to put up with for a shitload of time.
Then you have to cart them 160 at a time to the shop. That is more trouble than it is worth.