Our local rental association keeps a list of Unlawful Detainers that were filed, but it is printed on a month-to-month basis.

If they can move quickly and avoid eviction/unlawful detainer on their legal record, it will be better for both of you. 

I tell them that I fully intend to file an unlawful detainer and that they may not want that on their background search.

I was advised that the only way to proceed is with an unlawful detainer, and advised to proceed immediately.

Here in Arkansas, you would probably have to use the unlawful detainer process to evict the occupants of your newly acquired property.  

If a lease doesn't have fee shifting and cost shifting provisions, you should probably have an attorney properly draft your lease agreements going forward.That said, if you are relying on attorneys who are charging several thousand dollars for a simple unlawful detainer/conversion case, you are using the wrong attorney.

(note...she did not offer to pay rent) To proceed with an unlawful detainer I do not need to serve any notice but proceed directly to file.

And even then, it's a big risk for the tenant, because in the meantime, you can start eviction (which puts an unlawful detainer action on their eviction record) for nonpayment of rent.  

Anyone sick was brought to either the detainment center or hospital in a secure manner.

You will likely need to pursue the unlawful detainer action.