Money is too valuable to simply leave it sitting around doing nothing.

From a legal standpoint, if you have any litigation taken against you that either exceeds your insurance OR your insurance refuses to cover... it leaves everything under your personal name's exposed.

You could close the refi and the purchase in the same time, this way you will be allowed to refi and investment and purchase as owner occupied, otherwise you will be forced to refi owner occupied and leaves you with the purchase as an investment 

There are extra benifits to house hacking but numbers have to make sence for when you plan to leave said property. 

@Catherine Angle If you're thinking about wholesaling be sure to leave some meat on the bones!  

We fear the tenant will stop paying and never leave. 

If money is an issue, right now leave it as it is, and do it when you make some money from the venture. 

How / why is she leaving the previous place?

Like @Mary Mitchell my vacancy rate in Brooklyn, NYC, is effectively ZERO.I have been owning rentals for 21 years, currently have almost 30 apts with about 70 tenants.I estimate that I probably lost around 5 months of actual rent in all of these years.The vacancy rates are so low, it is SUB-4%.Normally, I will get a 45 day notice from the tenant leaving.

This is very likely a tenant that will leave when presented with having to pay market rents.