Other than oxybutynin or mirabegron, what pharmacological and non-pharmacological treatments would you consider for increased urinary frequency (not caused by infection, medications, or resulting in incontinence)?

There are a lot of other treatment modalities, all with benefits and potential side effects to weigh. The place to start, of course, is with behavioral modifications like afternoon/evening fluid management, caffeine reduction, timed voiding, urgency suppression techniques ("biofeedback"), and pelvic floor muscle training. Although these have limited efficacy, they are by far the safest.

For patients with refractory symptoms in whom you don't want to use either of these medications or their class...