I think you have a better understanding of the situation than we do. All I can really add is the IRS definition of a deductible business expense.
To be deductible, a business expense must be both ordinary and necessary. An ordinary expense is one that is common and accepted in your trade or business. A necessary expense is one that is helpful and appropriate for your trade or business. An expense does not have to be indispensable to be considered necessary.
Since undergoing therapy is, from what I understand, a requirement to be able to give therapy to others (keep your own house in order, so to speak), it seems to fit the definition of being both ordinary and necessary in that particular line of work.
Sometimes, if the circumstance fit, job-related education can be deducted either as a training expense or taken as a personal educational expense for tuition credits, and there is nothing that says someone whose expenses meet both definitions can't choose the more lucrative treatment. Similarly, I would say that if therapy is both a personal medical expense (itemized deduction subject to the 7.5% rule) and also an ordinary and necessary business expense, there's no reason you can't take the more favorable treatment.
Your proof, if audited, would be whatever documentation you have from various professional organizations showing that therapy is something you are supposed to do to maintain yourself in good professional standing.
