As I see things, my options are: (i) eat the cost; (ii) have seller adjust the purchase price down by some agreed upon amount; (iii) have seller write a check for the missing security deposits; or (iv) have inherited tenants pay a security deposit when we take over the property.

The problem you may encounter is this will eat into your profits given the small scale.I know what mean about the challenge of going after a "turnaround project" that is remote...  

Some will have a lot of kids who get out of the car drinking red pop and eating chips.

Your example is 101,750 a year cash flow over the 20 year period you mentioned....and as I noted you are basically eating your principal all that time and have little left when you sell at that point....NNN leases are out.From your example:"$2,035,000 Accumulated Cash Flow (NOI)"

People who are against Condos usually say this:The HOA will eat up a lot of your profit.  

You need a new property manager.The "50% rule" is a rule of thumb that say of the gross scheduled rents, expenses, vacancy and capital expenditures will eat up about 50%. 

What if it's sat on the market cause the seller really just wants to have his cake and eat it too?

I will humbly eat crow if you provide details.

Will the costs eat me alive?

There is obviously more risk with rehab and maintenance costs eating into your margin, but our team is pretty competent in assessing the risk and dealing with the work.