At the very least, a new line of credit is going to provide a small hit to your credit score and they may have an alternative solution or the refi may not be necessary at all to qualify.

But failing that possibility, would not an alternative be to keep that amount out of the reinvestment, declare it as taxable income from which I would deduct the same amount as an expense?

There are zero alternatives.  

Working on alternative to that which is fair to all involved.

So later in life I became an auctioneer, that education and experience gave me the confidence to create my little C&R system.I would control a property with some alternative creative contract clauses with full disclosures and I would offer the property immediately for sale using a reserve public auction.

It was my stove so no one to call but the repair man (who owed me a favor, so he fit me in and he had the replacement part on his truck).  

An alternative would be to raise some Joint Venture partners.  

I just became a member of bigger pockets and hope that this can be an outlet to connect to individuals who could provide strategies for locating sources of alternative financing for people like myself, who are just starting out.As stated above I am still young and interested in buy and holds that yield a consistent monthly cash flow.

Your other alternative is to speak with a mortgage broker and let them do this legwork for you.

The other neighbor, in the house next door, calls me to complain about them parking the tow trucks in the driveway because he's a gumpy old pot head.