Better Mortgage says they will only do a soft pull of my credit in order to give me a customized rates table and loan estimate.

That way they don’t feel like they’re leaving money on the table.

If you get rid of the PMI and bring money to the table, you can easily achieve that.

The problem is when you break the law, don't follow code, use under the table workers, illegal workers, ignore reported problems, gross negligence, etc.

But if you decide to continue holding after that point you'll have the 1031 option.I'm a big fan of tax free and taking chips off the table. 

Now I think your best option is to lay it all out on the table to them, and give them the choice to move out or deal with updates and rent increase.

I have an offer on the table for a home that is still tenant occupied.

Basements are prone to water penetration and leaks, from either external sources (rainwater, gutters and leaders,  grading, underground water table) and internal (burst plumbing pipes, water heaters leaking, washing machines leaking).

Once, that's on the table shift to what has really transpired and the events (facts) that have lead to your frustration.  

You need to bring some sort of value to the table.