I can't speak to NJ, but I know right out of the gate in NYC most multifamily sellers are averse to accepting a low downpayment offer (especially FHA).

I agree there may be times to lower the rent, but in my cities, county and generally state I have found that to be rare   Other parts of the country have different economic, real estate and supply & demand situations.Ultimately it is the market, laws & condition that determine what rent is appropriate and what the community will accept. 

Rather than accept an offer to cash out (offer restricted by current appraised value which because of recent vacancies was low) I chose to sell on a wrap around note.

There is nothing wrong with FHA, but most real estate pros would agree that if you are trying to get a seller to accept an offer when there are other competing offers, a conventional loan offer is going to usually be more favorable than an FHA offer at the same price.   

Could that keep you out of multiple offers or force you to accept a lower offer to sell?

If they don't want you in the property they can offer you compensation for your troubles, doesn't necessarily mean you have to accept it.

The only exception I would accept here is that if it's your first time....or maybe the property is in a rural area...then there would be some allowance to the lender.

As I continue to save and approach an acceptable down payment threshold, I am debating a few things and looking for some advice/insight. 1.

Some offers might get ignored or outright refused, but all it takes is one offer to get accepted or countered to start negotiations. 

Many investors I work with from the Bay Area are purchasing here and many people from the Bay Area are relocating here as work from home becomes more accepted.