Now I'm left wondering whether it's best to lower the price to get the property off my hands asap or to make some costly improvements that will probably neutralize any increase in value.

When we do the construction loan, we'll take the cost you paid for your lot, your soft costs (plans, permits, property prep, etc) and add it to the build costs (keep in mind, we'll make sure those amounts are fluffed and that they make sense).

My properties are listed on both, but I keep spreadsheets on "issues" their resolution and how much it cost to resolve them. 

Finally, closing costs were reasonable.Cons-  Quality control of closing docs. 

Costs a fraction of the funds compared to hiring a cold call agency.

I’ve requested financial statements, tax history, utility costs, and information on the property management company.

You're going to need 20% down plus closing costs for just about any loan product out there, DSCR included.

looking to place a bid on a trustee sale in los angeles under the sb10497 law for potential tenant bid.

Management costs would be yours not their current. 

Otherwise, you could potentially do a Debt-Service Coverage Ratio purchase or refinance to get the necessary funds which would be a cashflow based lending option for investments.