So not adding to our debt, but pocketing cash and paying off debt that way.What would you do and why?

Your credit score will help - Lenders don't want to lend to owners with history of bad debt, etc.  

Additionally, my credit history is fairly young (although good, between 720 -770 depending on where I look) since I only moved to the US three years ago, I have no consumer-, student-, or car-debt, 100% payment history and no derogatory marks, but the Banks I inquired at either don't have LOC for investment properties at all, or my income is considered to low on paper, and I am trying to access some of the equity sittingThanks in advance for taking the time to answer if you can help!

Unless your credit is not great, or your debt to income ratio is throwing you off.

If you want to leverage your cash, you can purchase, say, $5 million in assets with 60% debt. 

It's better to pay off debt with the money if you want to reduce your DTI.

While at the same time having already used the refi money for another property somewhere els.You don't specifically have to take out the same amount of debt as you have in your old property. 

If each co-owner has an undivided half interest then have the co-owner who wants to sell, write out a detailed affidavit with any available documentation -listing all of the expenses that each co-owner has paid for mortgage, taxes, insurance, maintenance etc, during the last three years (or whatever your local statute of limitations is to file for unpaid debt). 

I'll double down on the fact that unless sellers are in the real estate industry or have some kind of investment experience, they are unlikely to take the burden of servicing the debt.

Note that the 1% rule in most cases will not meet a commercial lenders debt coverage requirements, which is telling-----The 1% rule is only a rule of thumb, and in most markets doesn't cash flow well enough either.