Alternatively, you can buy green dye that you spray on the grass (I kid you not-it is eco and pet friendly).

Drywall would be a better alternative I think if you were flipping or in a A-class neighborhood.

Given I can’t evict her now because of coronavirus and she’s not answering my calls about cash for keys any other alternative I have?

An alternative is to refi your current mortgage balance and then get a HELOC.

I am neither a realtor nor a mortgage lender so I have no alternative conflict of interest and I don't have a training program that I can sell you. 

Does it makes sense to pass on a property you plan on holding over the foreseeable future due to not getting the FHA loan or does it make sense to close with an alternative form of financing leaving other exit strategies on the table?

Cash out refi's may increase your monthly payment - once you to do this you are locked in.Another alternative to consider is a HELOC.

Alternatively, I was considering selling my unit and using the profits to invest in two properties: a new primary residence and an investment property. 

Alternately Charge them full months rent and deposit upon occupancy and charge them prorated rent  for August but paid the next month on Sept 1.   

Alternately, you could encapsulate it so any asbestos fibers cannot escape.