How to clean my jetted tub when commercial cleaners fail?
I have seen some horrible garden or jetted tubs growing stuff and that was one of the reasons I got 1 place at 1/4 market value on a short sale. Drain the tub ether purchase several gallons of liquid chlorine or a couple gallons of bleach. 

First fill the tub with plain water as full as practical) and run the pump you want to get rid of any cleaning chemical residue drain, you may want to do this 2x if your last treatment is not removed. Fill the tub with water and add 2 full gallons of bleach or chlorine, turn the pump on and the exhaust fan. Let run for 1 hour, let sit for an hour (this allows the strong chlorine to get in the air passages for the bubbles and kill anything in there. Run the pump for another hour or longer. 
Drain the tub and fill with cold water, run the pump for a couple of minutes and drain. Fill again run then drain again. 

If this does not clear it up get 1/2 gallon of 25% hydrogen peroxide. Fill the tub with hot water and add the peroxide, the peroxide will increase the heat in the water, run , let sit like before for a few cycles drain and rinse.

I used this method on a home that had a sewer back up into the tub and stuff was growing on the surface yuk. I replaced the broken drain line and over night the tub was like new after polishing the surface. Total cost was approximately 30$ and about 6 hours filling and draining.