I had initially planned to finance the rehab with cash and creative financing (lines of credit and such), and then financing it all through a bank.

I have no one to blame but myself for not participating in financial decision making, carrying credit card balances, being ignorant of our retirement savings and mortgage details, having no personal plan for my own financial future, and never creating a budget.

Is it ok for me to use a loan or low-interest credit line of my own to pay the mortgage on the duplex before I get renters in it?

It's cash in pocket or a credit card swiped on my Square Reader when I collect rent.

I have tried with two smaller lenders(National Bank of Arizona and OneAZ Credit Union) and they have both dragged it out for several months before deciding they wouldn't do the loan for what I perceived to be fairly silly reasons(Management didn't like that the tenant had only been in for 1 year, Management didn't like that the structure used to be a residence, management didn't like that 3 years ago I took a loss in a completely unrelated business etc.)I am hoping that someone out there has had some success purchasing or refinancing commercial property like this in AZ and can put me in touch with someone who actually completes deals like this.

I have great credit ~790 (last I checked).

But typically you need a decent Credit rating over 700 for good interest rates.  

I don’t have cash but I know I can get approved for a line of credit that would cover my down payment.

This is low work on your part and will put it on their credit report for prospective new landlords to see.

The average rental in that area actually little bit lower than you expected, plus the turn over rate is higher as well due to tenants creditability.