J.K.
I think you are correct that your problems start with not sealing the limestone. To get the best result, the stone would have to be professionally cleaned and then sealed. They would use a series of grinding to bring the stone to a fresh condition then polish it and seal it. Natural stone is like a sponge that soaks up everything and it is very hard to remove dirt from it's pores. You could try calling tile suppliers in your area for suggestions on cleaners to try or a company to clean and seal your shower. THe good news it that once it is sealed, it will be easier to maintain. Good luck.