I do not have a lot of capital at my disposal to get into a top-notch neighborhood or a higher priced property, but am looking to put the little I have to work and build from there. 

Anything left behind can be disposed of on the 11th in my opinion.

THe tenants admitted disposing paper towels into the toilet when cleaning 2 days prior.

You might consider engaging an attorney to draft a "Mutual Agreement to Terminate Lease" or something to that effect that is valid in your state.A simple 1-2 page agreement outlining that 1) she has surrendered or abandoned the premises, 2) you have her permission to dispose of her personal property, 3) and you have her permission to liquidate her deposit for past due rent, can save you tons of potential legal headaches down the road, and would likely be far less expensive and time consuming than an eviction.Forget trying to collect on the remaining months of the existing lease.

Changing something like a garbage disposal is a pretty good starting point.

Though there are some creative solutions to this and other issues - Fellow BP member  @Dave Foster is the man to talk to about the 1031 side of things, and he has a lot of tools at his disposal to help with all of the above. 

You can always dispose or sell the older unit.  

He’s done laminent flooring, I pulled up the carpet and pad and disposed of it to assist in my costs and have it ready for him to jump in.

Have them collect anything they wish to keep, and get in writing permission for you to dispose (or do whatever) with anything they leave in the house after signing the agreement.

1 - Any qualified charitable organization that aligns with his values, and accepts donations of real estate.2 - If he donates the land to a qualified organization he wouldn't realize gain or loss on disposal, instead he'd get a charitable contribution deduction for the fair market value of the land.