There are limited exceptions to that for single member LLCs, also depends on your liquidity or ability to refinance as well. 

The down side in this case is you lose the ability to negotiate the price after inspections.

We have a lot of debt and a limited ability to stimulate our economy due to interest rates being so low.

My question is, if I get a bank to refinance the deal immediately after purchase would it make sense to cut a 20k check for the ability to have a cash offer?

It also ignores the ability to "swap 'till you drop" and defer those CG taxes indefinitely. 

I also think that there are definitely some tools that can help with managing rent payments moving forward (would make it much easier on you as you submit those payments through to your LL) and can provide additional capabilities which makes it an easier sell on your end (ie. their ability to report on-time rent payments to the credit bureaus; this can create an added incentive for making sure the LL gets signed up).

While the scale of this health-related emergency is unprecedented, our ability to function in the face of sequestration is not. 

The contractor is probably outside of his ability to lien your property, so he can't tie up your equity, which leaves bringing a lawsuit - possibly small claims. 

The lender is one of the most important elements of your team, and these questions are very basic.

Does it rob me of the ability to pay off a smaller loan for one house and then cash flow that house or does this somehow even out when I combine the loans?