Would a home equity loan be a viable option in this situation, especially in regards to eliminating some of the red tape I'm running into with a refinancing an scorp-owned property?

There are more buyers for SF homes, but Multifamily properties typically cash flow better as you mentioned. 

Context matters: for some apartment buildings that compete head to head with a very similar property just down the street, this may be a good strategy.We rent premium single family homes and I have never offered an incentive.

Is the same thing happening in the neighbor's homes? 

I am in the same boat of either 1031 exchange or refi some of my small multi's to purchase a larger complex.

Right now, I'm exploring investing into a mobile home park.

Why not take out a smaller mortgage on the home and use some of that money to buy a second home?  

Sometimes larger portfolios for sale will have owner financing terms a seller is willing to accept (always negotiable). 

You typically will see small banks/credit unions probably wouldn't be able to out-of-state, but otherwise any mid-size company or larger should be able to.

If you have a larger portfolio, are you still self managing?