Thanks for asking, I was worried I left some clarity out in my haste! I had intended for all cards to be shuffled and hands re-dealt at the end of each turn, Including the cards left over in your hand. This does mean that you end up shuffling a lot, unfortunately.
If you are only playing with two players, It's probably fine to just use a discard pile for the previous hands and just re-deal from the remaining deck a few times before completely reshuffling as the potential to effect any outcomes by counting cards is pretty low. Whatever makes playing smoother for you!