Congratulations on your new position!

It sounds like that's the only opening she has at the moment but can foresee a time when a slot might open up in the future to get you to once a week. She can't bump another client out of their slot to accommodate you; you realize that wouldn't be right for another client but your anxiety about the change is understandable. It can be okay eventually; I suspect that's what she meant. She can't exactly wave a magic wand and immediately adjust everyone's schedule but she seems willing to work toward that adjustment -- it may just take a bit of time.

Why not try the every other week scenario in the meantime. You can look for another T if you wish, but your current T will still be in the mix in the interim. Who knows? You may find every other week works okay. Or, maybe things will change with her schedule in a reasonable amount of time to get you back to once a week.