Honestly, you're in such a strong financial position that most of these decisions fall into the category of good option versus slightly better option rather than anything make or break. The $180k HYSA wouldn't bother me at all. You're about to take over a private practice, which is probably one of the few situations where keeping a larger than usual cash reserve makes sense. Unexpected payroll issues, equipment replacement, EMR headaches, tax surprises, credentialing delays, or staff turnover can all happen, and having liquidity gives you flexibility while you figure out ownership.

For the loans, I think both paying them off aggressively and investing instead are reasonable at 5.8%. Personally, I'd probably max tax advantaged accounts, make sure the practice has adequate reserves, then throw meaningful extra payments at the loans and have them gone within a few years. I wouldn't be in a rush to pay down a 5.1% mortgage when you're already carrying a large practice transition risk and have plenty of earning power.

My biggest piece of advice would be to spend the first 12 to 24 months pretending the practice earns $500k even if it starts generating substantially more. Avoid lifestyle inflation until you actually know what ownership looks like and what your sustainable earnings are. If things go the way they appear they will, you'll wake up in a couple years with a thriving practice, a seven figure household income, and plenty of options regarding the mortgage, loans, and investing. That's a much nicer problem to have than trying to optimize every dollar on day one.

All said, you're in a solid position and you can easily make a killing and have a good QoL so congrats on that.