The fact you have 'no-title' for the D-W, and as you mentioned previously there are no lien-holders to be found - means you are set up marvelously to call the D-W 'abandoned property' - this happens frequently, and the State of Texas has a process that will create a new title (since it is personal property, not part of the land) - that will be in your name, and will be sell-able after that as it will be a good marketable title from then on. 

We’ve reached out to a few property owners in an attempt to purchase some of the abandoned ones.

What do y’all do with tenant abandoned, roach infested, household goods?  

It was abandoned and boarded up.

Not so in every case but it is another tip in the toolbox to help in finding abandoned house owners.

Its that simple, and that can and will cause, transfer issues unless released properly (foreclosure, Probate, Estate, Properties of State, Divorces, Abandoned Properties, ED, Deed in lieu's, etc...  

is an abandoned home a zoning issue?

so I came across an abandones property, took the address swnt it to my title co.

Now Electric D/C's  and mail route abandoned reports.....  

However after the first week they stop picking up their phone.I also use Intelius to skip trace leads and abandon homes I find doorknocking and driving for dollars.