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Bromine tabs in a floating feeder usually don't last much longer than a week or so if there is no bather load, but if the spa is used the bromine level can get too low. Does this spa have an ozonator? If it does, then an initial bromide bank may not have been properly established.
As for decontamination, that requires a superchlorination or use of
Spa System Flush or both, but either way you'll drain/refill after doing so. Though you could just do a shock to a higher chlorine/bromine level, that may not be enough and personally I wouldn't take the chance given the infections that occurred. When the sanitizer level gets to near-zero, biofilms can form and those are very resistant to normal or even shock chlorine/bromine levels (especially in spas), hence the more extreme methods for removal.
4 cups of 6% bleach in 350 gallons is 44 ppm FC. That is not bad, but the full decontamination procedure described in
this post uses 100 ppm chlorine. Since you don't know the history of this tub, the most extreme approach would first use the Spa System Flush, then drain/refill, then do the decontamination with 100 ppm chlorine, then drain/refill. This may be overkill, but it will most certainly get rid of any biofilms and kill any lingering bacteria.