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You have certainly tried the more common anti-anxiety approaches to calming stressed cats, which clearly has not provided adequate results. It sounds to me like the Balinese may not be very social and amenable to coexistence with another cat. Her fearful and subsequently hostile reaction to your Siamese only encourages him to provoke her. Whether being outright combative or reacting out of stress and fear, cats become themselves stressed when perceiving extremes of emotion from one another...your Siamese's overbearing/aggressive reaction is how he deals with her demeanor.
You had asked about a time frame whereby major hostilities should abate, and there is a good answer to that...this has actually been studied quite heavily in veterinary behavioral medicine: 60 days. By this period of being integrated, if 2 cats have not learned to generally accept one another - not necessarily be best buddies, but have some tolerance of one another - they are not likely to. At this stage, you can either consider re-homing the Balinese, or think about treating them with an anxiolytic.
The most popular anxiolytic used in cats for chronic stress and behavioral problems, is amitriptylline, being well established in feline behavioral medicine as safe, effective, and cost effective. Amitriptylline works by raising seratonin levels in the brain, thereby reducing feelings of anxiety and fear. It can be very helpful for kitties with behavioral issues, and after several months of having achieved desired results, sometimes patients can be successfully weaned off the medication. If interested, you can talk to your veterinarian about dosing your cats.