While I don’t have debt other than the mortgage on my current primary residence, I don’t bring in a ton of money, either, so throwing down $100k down payments are out, at the moment!

That said, we put our homes at risk with the higher debt service. 

I learned quite a bit with the purchase including how much you can really leverage your debt in order to limit your liquidity exposure.

On a property you intend to hold long-term, replacing long-term debt with short-term debt makes no sense to me. 

A DSCR (Debt Service Coverage Ratio) loan is exactly that!

Would a line of credit be seen as a debt when the underwriter is reviewing your finances?

If it's truly valued at $400k, you could pull out up to $300k with no tax implications whatsoever (you'd be taking on debt, not incurring a capital gain).With regards to depreciation, engage a great CPA who understand and specializes in real estate investing, and ask them if it's possible to use a cost segregation study to take accelerated depreciation.

Might as well take the slightly higher payment from day one and start paying down the note immediately since your tenants are the ones servicing the debt every month.

How much debt do you have? 

If they did the Government debt would be more unsustainable than it is now.