Could you merge LLC-B and LLC-A before the sales process and do a cleaner exchange? 

Your question is a little confusing; what do you mean how do you do STR with a mortgage?

I'll just do long term rental. 

What documents do they require, what credit scores do they allow, how do they verify previous rental history, etc.?

In order to transfer title/deed into an LLC, you need to contact a Title company and you will also need to refinance (see point 3. as to why you will need to refinance - if you do not you will have the mortgage called)2. 

What kind of investing do you want to do?

However, if you qualify for Real Estate Professional Status (REPS) or do STR, you may offset W2 income with rental losses.

Do hard money lenders typically require a down payment?

Do your research, set clear goals, and decide on a strategy that works for you.

Do you have any remedies?