Another big issue up here is unresolved basement leaking/moisture problems.

I won't even discuss the plastic sheeting and gobs of silicone he used to "fix" a leak under the sink. 

We've dealt with a lot of rain and water damage, and the usual fixes didn't work until we did an investigation with an infrared meter into the source of the leaks.

My property management company said they can take care of the lease, collect move in funds, give supporting docs (like certificate of rental suitability), lead paint disclosure, move in inspection, etc for $600 but I'm wondering if I should just do it myself?

As mentioned before I just dropped $500 on a doc with a local attorney.

One way to avoid taking the liability of the old LLC and the doc stamp in certain states, is to use a new LLC created by the current owner.

You will still be recovering from closing costs unless house appreciates.If you find a good deal that you are absolutely sure that is going to appreciate then go ahead, otherwise let your landlord take care of leaks :D))

Keep in mind, this all started with a small leak in the basement plumbing of a very old house:Tenant reported she could hear a leak in the basement when she did laundry. 

We were able to reach out upstairs neighbor, who owns the unit and has been residing in Florida, who reached out to her family member to let us in the unit to see where the leak was coming from.

My example: In the Phoenix AZ area, the builder special AC had been causing problems for a few years and then started leaking through the ceiling.