Step one is to determine the required strength you need, which will depend on the geometry of the load applied to each joist. In this case, you have a combination of a 1000 lb tub plus framing dead load plus live load from humans. This is an unusual case where it is probably necessary to perform mathematical computations to determine the maximum moment on your joists to determine how many extra ones, and of what type, you need.
You have indicated that you can only get 2x6 joists in due to clearance restrictions. However, your span is only about 7 feet, so you may well be able to use 2x6 joists, provided they are appropriately spaced. There is nothing wrong with I joists, however they may not be necessary. Like I say, you have to apply the loads and see what the moment on the joists turns out to be. If you are unable to perform the computations, you may need to get an engineer to do the work for you, or perhaps a contractor or a lumber yard can help. Unfortunately this is a case where you cannot use tables, due to the heavy point load combined with the distributed live and dead load.