Tax sales are a balancing act among (1) the need of government to collect property taxes and, if owners will not pay then, then to provide incentives for investors to purchase the tax rights and (2) investors, who need an attractive return for the risk they are taking, and (3) citizen taxpayers, who should not lose their property and all equity because of small debts and perhaps temporary or at least relatively short term financial difficulties.

Like if they were required to pay 90% of their appraised value to purchase the property at the seller’s option?

Second, having $40k and trying to purchase a multifam in NYC is not going to get you far. 

Within days, I received several calls and emails with offers to buy under PURCHASE CONTRACT AND ESCROW INSTRUCTIONS.

However, there's no AC and heat there and I have already purchased min splits air conditioners and an electrician has also laid the lines for me.

In my market, agents/investors/wholesalers pitching creative financing get this objection as well.They typically have a 2nd offer (usually much lower purchase price) for the owner to be able to accept now and cash out. 

That means you can spend up to $70,000 on the purchase price and renovations and it would still be considered a good deal, according to the 70% rule. 

However, the house is not selling, having me consider more than once to rent it out, tap into my equity, and purchase a fixer-upper triplex in another part of town (where I would also live).

Purchase price: $60,000 Cash invested: $20,000 Sale price: $240,000 Lakefront duplex Denver Colorado.

Purchase price: $560,000 Cash invested: $55,000 The strategy going in was part live-in-flip, and part ADU value add.