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?

So before dismissing your options, you may want to consult an investor friendly Lender who is an out of the box thinker.

Don't be so quick to indebt your paid off townhome until your learn creative financing and review all your options.

Outside of raising money from others or seller financing, I am looking to see if there are private or other lending options that could cover 10-20% of a downpayment on these loans with a shorter loan term of say 5 years.

My vote is option one.  

Today I had a heater issue and snow company that was late handling commercial before residential so we ended up clearing it.Open to each option.

@Jerry Chilimidos,Here is a list of lenders who specialize in lending to IRAs and 401Ks:https://www.biggerpockets.com/member-blogs/2810/50272-list-o...I don't know where your rentals are located and how they are performing but selling might be an option vs doing cash-out refi.I would certainly consider option C.

House hacking is probably your best option.

So all of the gain and depreciation recapture are initially still tax deferred.However, like Joe said, the down side is later when sold  you lose the 1031 option. the client will pay tax on all gain and depreciation recaptured from before the 1031 also. 

I’m considering doing a cash-out refinance, not sure what the best options is , to use the rental property or the rehab property.