As I sit here thinking about creative ways to fund a deal, including hard money, I have come across the idea of a Solo 401K plan and loaning to myself from the plan.Key facts that I can find are:  5-year term (normal prin+interest payments required at least quarterly), Larger of $50K or 50% of vested balance is the max loan, no credit check or specificity required about intended use of funds, failure to make payments/payoff on time are that plan treats it as a taxable distribution (early in my case), can loan at a reasonable interest rate which sounds like can be a prime+ type rate.....last WSJ prime was 3/22/18 at 4.75%. 

The tax deferred nature of appreciation and the long term low-risk history of holding New York property make buy-and-hold at cash flow neutral, or even negative, compelling for investors with other primary sources of taxable income.

In a summary, your worst case taxable assessed value can be $6,000, $6,360, and $6,741 in year 1, 2 and 3 respectively. 

It is absolutely possible to ignore "taxable" income. 

Would it, or the proportional proceeds, become taxable?

The gain you already had is taxable.

This should take into account the interest earned and the discount amount as income and become taxable. 

However, for the taxable account, what would be my options to limit my tax basis (as well, how would I be able to calculate what my capital gains would be - is there a simple way to do so?)?

That would void the 1031 and make the whole thing taxable.

The only difference between retirement accounts and taxable accounts is taxation.