Cooking vs. dishes clean-up is the hardest in a reno; plan meals w/easiest clean-up in mind. Bussing bins are your friend since they are much larger than dishpans. We got two of them; one held the dish drainer. We have a utility sink in our basement so never had to resort to the bathroom/bathtub, but if I were in your position, I would fill the bus bin in the bathtub, then balance it over the bathroom sink to do the dishes.
We emptied bookcases of books, then used them to store kitchen stuff we would be using during the reno. Also kept utensils and flatware stacked in the old drawers; it kept the stuff easy to locate. Since we're Asian, we use a rice cooker, so that appliance simplified cooking. Also used electric frying pan and MW since the hot plate we borrowed was unbelievably wimpy. You should be able to pick up all manner of small appliances at thrift stores and garage sales, not that you want to live on chocolate fountains and fondue. I remember hearing about crockpot disposeable liners; crockpots are a pain to clean so if I wanted to use one it would be a low aggravation solution.
Your kitchen seems to be coming along fairly quickly!