We also bought during the first-time homebuyers credit era, so we got a check for 10% of the purchase price back with our taxes, and if I remember correctly, we used an FHA loan with 3.5% down.

I've got excellent credit at the moment and a job with six figure income (however much lower after taxes/student loans/primary mortgage), would this help gain what I want with a lender?

During that time, I also had 2 mortgages that were successfully modified--but as a result my credit scores have suffered and dipped to the low 600's.

ITT students might be able to transfer their federal loan credits elsewhere or possibly have them canceled.

. $3400, maybe take out cash advance on my credit cards $2500, and do a cash out refinance to get the equity out of my house. 

If little or no equity, probate costs will likely outweigh the benefits of trying to save the house so an arrangement to get cash for keys from lender in return for a dignified relocation plan/timing would be preferable,

Income and credit play a part, but not as much like a conventional lender.Get a HML, fix, flip, repeat.

NOW, if we are to have the HOA responsible for the interior of each of the units as well, here are the eminent problems I foresee:    - owners will be even more careless and act irresponsibly for their units since they don't pay for the repairs of the interior of their units    - because many of the owners rent their units (technically they sublease), they will be even less incentivized to maintain their units    - the HOA pays for all maintenance and repairs of units and owners get the benefit of rent    - repairs/maintenance of units is not properly proportioned to their respective owners, meaning that there is no incentive to keep my property up because any repairs will come out of the pocket of all other owners    - this penalizes good owners and rewards slummy owners    - this will put the owner residents at a big disadvantage because the owners who rent their units will cause maintenance fees to increase for all owners, especially due to high turnover    --> in Summary, this is a straight example of socialist-style system (I know, my family immigrated to the US from the USSR) and it will just sink our whole Co-op.  

So I am trying to run numbers on a few larger apt. buildings and the expenses the owners have given me are obviously inflated for tax benefits.  

Your options would be a cash out refi, or a HELOC (home equity line of credit).