Is carrying it on my card worse for credit than carrying it on the HELOC? 

Consider 401k loans and 0% interest for a year credit card loans too.

My business partner and I have a joint LLC (shared business bank accounts / credit cards / etc) - pretty standard stuff.

Now if I can just find my credit card…… 

Both Prosper and Lending Club offer loans big enough to cover your 50% down payment.Something I would never recommend to most people, but as a last resort -- if you absolutely knew you COULD pay it off any time you wanted, you could put the down payment or at least a big chunk of it on a credit card and float it between 0% balance transfer offers until you get it paid off.

C-corp is too complicated and cumbersome in my opinion.)Open the LLC, get your EIN number, and then open your checking account and first credit card with one bank. 

I really like stessa because it links with my business credit card and checking account.

Almost all documents that are needed for closing (Bank, Credit Card statements, brokerage accounts, etc) are on line.  

From there, you can set up a virtual account for each property that can also have a virtual card attached to it.

I would house hack till I die if I could but unfortunately it is not in the cards for now.