After 7 years, the remaining principal balance ($425k) would be owed immediately. 

If that were the case, I would be more a bit more gung-ho about moving forward but now that I have to do this principal pay down, it has me doing a much deeper analysis to make sure this still makes sense.

Former mediator here who worked under a principal empowerment model in MA.

So this will be a slightly lengthy answer so bear with me.Based on your current situation with your Mortgage and your HELOC the max Combined loan to Value(CLTV) for a Principal Residence cash-out refi is 80% in a 1 unit and 75% in a 2-4 unit, In a investment property cash-out refi the CLTV on a 1 unit is 75% and 2-4 unit is 70% .

@Anthony Mikolich you get a deduction for the mortgage interest that you are paying, not the principal so taxes will likely go up very slightly because of the mortgage being paid off.If you've the house as a rental for 27.5 years (mot including the primary residence years), the depreciation of the house will be complete and taxes likely will go up.

You get 0% ROI for paying rent while purchasing will give you several benefits including asset appreciation, principal pay down, and tax benefits/ depreciation.Once you move out in a couple of years, you can re-evaluate the property to determine if it makes sense to keep it as a rental (in which case you still get all of the above benefits; however, the tenant is now covering the principal pay down), or sell it and capture the potential gains from the property's appreciation.

I can't help with a principal residence however.

During the 08 crisis I qualified for a HAMP loan mod that included a large principal reduction as my home was 50% below purchase price.

If you do not own a home, I would recommend you use the funds as a down payment on a light fixer which can serve as your principal residence for at least 2-3 years. 

Even if you buy in an LLC, it takes like five seconds to find out who the principal is.