HELOCS do exist for rental properties but you are usually capped at 65-70ltv and these will most likely require a full underwrite that takes into consideration taxes, income, dti and all the normal quasi-associated red tape.

Neither of these require income verification and much easier to navigate versus conventional. 

Is it wise to look at places you can afford alone, or use rental income to offset what you can afford?

I’m looking to invest in a portfolio of multifamily properties to eventually replace my full time income.

However, one of our objectives is to reduce the tax burden we face on our W2 income.

Nevada has no state income tax and the 4th lowest property taxes in the United States. 

Which I would think is surrendering the rights due to the inconsistency of income or no income or wages? 

Indeed, and depending on a variety of factors you can even use them to offset your w2 income 

If you're at a loss and paying off the shortage still puts you at a loss I think your best bet is selling, or seeing how you can get more income from current rents by making it mid term/seasonal or an air bnb. 

Census data - median household income, employment stats, bachelors degree percentages, crime, vacancy rates, appreciation2.