The chlorine-free Spa Shock is likely potassium monopersulfate (MPS).
The easiest way to tell if you have a working ozonator in a bromine spa is to see if bromine is maintained in between soaks when the spa is not used for days even when you don't have any bromine tabs. Also, ozonators don't usually work for 8 years so even if you have one it may no longer be working. You can probably assume you don't have one.
So with bromine you usually need to use chlorine once in a while to keep the water clear. Using MPS isn't always enough. The WRI would be roughly the same formula as the Dichlor-only one (the one with the 1/9th factor when calculated in person-hours). The Jacuzzi J-345 specifications
say it is 370 gallons so with your changing the water every 4 months (assuming it needs changing that often) implies (1/9) * (370) / (4*30) = 0.34 person-hours per day so roughly one person soaking for 20 minutes every day. How often do you use your spa and for how long are the soaks and how many people in the spa?