If you are both agreeable that she has moved out then take possession and do your turnover work...I would go as far as offering her "fair market value" for her possessions so there is no desire for her to pursue them...then you can trash them or whatever....it sounds like you are self-imposing some unnecessary obstacles...

You may have possession, but not a clean title. 

If they decide not to appeal, they still have possession of your property until the Sheriff gets around to scheduling the Writ of Removal... which they will likely protest on the same grounds.I would not want to be in the courtroom when the judge/magistrate hears you accepted more/less full payment and evicted anyway. 

Once I had possession of the property I had one of the contractors that I work with go in and do a full rehab.

Kenneth Wright, Presiding Judge of the First Municipal District of the Circuit Court of Cook County issued General Order 2017-01 which sets the dates and terms for the 2017 moratorium on the enforcement of orders for possession in forcible entry and detainer eviction cases in Cook County.

Just paying the taxes gives you no legal leg up on owning the property.....that is misinformation.....maybe they are referring to Adberse Possession which wouldn’t apply in this situation typically......state laws are specific.You are going to have to talk to a probate attorney in Your state.  

Myself I have a building  background and possess journey level skill in almost all trades except maybe doing concrete work and I am also an architectural designer so I perfer properties that can be increased in value through forced appreciation and look for properties where the zoning, set back, and other requirements allow for adding square footage to a building but others perfer invest in turnkey properties already fully occupied whereas I like working with empty buildings. 

I assume that I can take possession (change locks etc) and perform structural repairs sufficient to bring it back to habitable standards but my question is does that include sprucing up the property itself ie tree trimming grass cutting and the like to maintain neighborhood norms?

Different people possess a different set of skills and opportunity will not smile equally on everyone, certainly not at the same time.

They also boarded up every entry to the property after I made repairs and forced possession back.