One option you have would be to switch your tub to bromine. Ozone reacts with bromide to create bromine so this could help keep your bromine level stable between soaks. You would dose with chlorine just the same after soaks, it will just activate the bromine which will then burn off the organics.
They do also make SWGs for hot tubs, which is another option. I would consider either to be a better option than using chlorine tablets in a hot tub since they will dissolve quicker and will overstabilize fairly quickly. It can be done, I just like the other options better.