What a difficult dilemma, having to decide between supporting physical and mental health! I know that this must be heart wrenching for you. I would bear in mind as you consider your alternatives that depression is also a life-threatening condition, and you know that the old med, while it was very effective for the asthma, definitely caused serious mood disruption. You don't know how well the new medication will control the asthma long-term, (remember, it might be fine!), but you do know that you are already seeing benefits in the mental health domain. As someone who has experienced both life-threatening asthma and psychological side effects from prescription meds, I personally would be more willing to deal with less-than-optimal control of asthma (though not at the hospitalized-every-month level) than with uncontrollable mood and mental changes that make me feel not myself.
Have you looked into anti-inflammatory dietary changes at all, and have you ever considered acupuncture as an adjunctive treatment? (Acupuncture has been repeatedly demonstrated to help control inflammation.) Both have been very helpful for me in reducing the frequency and severity of asthma attacks, to the point that my only current medication is a rescue inhaler that is used perhaps once or twice a year, if that.