You need an option contract not a standard agreement of sale.

Right now I am forced to take the standard deduction.

Only thing HUD cares about is does the property meet its standards

If you spend under the $16,000 they pay under the Actual Cash Value payment (i.e. no depreciation reimbursed) then you get to keep the remainder... so say you end up being able to get everything done for $14,000, then you get to keep the remaining $2,000 which is not technically a profit, just that you were able to do the repairs in a more cost-effective way than the standard market price.

The appraiser used much smaller homes than ours and added the incremental sqft at only $33/sqft, which must be some standard they use.

in a standard septic system it consists of a tank and leach lines that run out from the tank.

All that being said, the standard BiggerPockets.com mantra is that equity represents lost money and opportunity cost, there are plenty of voices that logically and coherently argue that side of the debate (who will be joining this thread shortly), so by all means weigh all options, figure out what works for you given your particular goals and risk tolerance, and there is no "one size fits all" solution. 

I’m on top of standard listings and price reductions - and am a pretty good negotiator, LOL.

That's the standard FNMA HomeStyle program you just described.

Industry standard is 10% per monthly rent for vacancy, repairs and maintenance and capital expenditures.