https://en.wikipedia.org/wiki/Adjustment_disorder
As a therapist yourself, DonaldsonBry, you're probably aware of this disorder, and that it usually occurs in reaction to a particular life stressor, major change or trauma.
In your wife's case however, she seems to respond in a extremely emotional, over-reactive manner to almost every life change she has experienced... and exhibits highly anxious, avoidant and overly-dependent behaviours to such "trigger" events.
In my view, the above - in conjunction with the fact that she has always been sexually repressed even before your marriage, and the fact that she shirks adult responsibilities, leaving you in an ersatz "care-giver" role - indicates some kind of inherent personality disorder and/or life-skills deficit that haven't yet been identified or treated.
In light of these long-standing anxious-avoidant, (co?)dependent behaviours, I do NOT think it likely that your wife will react or adjust well to you "trying it your way" as an experiment. Especially since she rejects the notion of therapy. Nor do I think you ought to just accept a sexless marriage for the during of your natural life.
Therefore, the only workable options seem to be either parting ways/separating/divorce... or as opalescent suggested, transitioning to a "companionate marriage" in which you agree to co-parent and live together or in close proximity, while only being married in a nominal sense. Your personal lives would be your own concern and would no longer intertwine. She would then be free of any obligation to be a sex partner and in turn you would be free to see other people away from the home. More or less like a DADT policy.