Why not just buy a new primary and rent out your current home.

Unless you negotiate a new contract or addendum with your PMC, they do NOT have to abide by any requests/demands you make that contradict what's written in the management contract.If they have in fact NOT followed the terms of their contract, then you'll want to send them something in writing pointing out the specific language in their contract that they violated and ask what they plan to do about it.If they fail to correct or address the issues, then you'll want to start looking for a new PMC.

I don't believe "waiting it out" is an effective strategy.

This would be my first real estate investment, making the decision even more critical.I understand that backing out would mean losing the $2,000 earnest deposit.

I really don't have the $23k down payment I'd need for a DSCR, and Texas wont let me HELOC the equity out of my other rentals. 

Those people are out there, you just need to find them.

IF you cashed out you'd walk away with around $400k. 

She refuses to pay rent and says she cant be out until April.

Would a cash out refi be under commercial terms since the property(s) are under LLC?

I think will find that out-of-state will be much more operationally challenged than local.