I want to refinance my lender out and get some kind of conventional loan so I can pay down the balance with the rental income.

Your best bet would be to learn through Youtube.

So no, you cannot refinance as part of this process.Sure, there are creative ways to do this but they make no sense here because they create unnecessary risk. 

Your best bet in the greater Phoenix market will be a four unit property, because it's tough to make the 2 and 3 unit properties cash flow with 25% down.

Timeline:Property 1 Purchased Jun 2016: Purchased for 5% down @ 255k, refinanced about a year later at @ 325k with some minor renovations completed, and got a HELOC Oct 2017 for 20k and had 20% equity in the property vs 5% when I had purchased Property 2: - Purchased in February 2018 for 192k and had it reappraised in March/April for $222,500 - This was super low based on comps and I asked for a review based on the brokers opinion of value as well and he said he could not review it- After this the lender informed me that he could not even do the refinance with the appraisal because my DTI was off- He recommended waiting a year or so until the rents from the new property show up on my tax return and to pay off some debt for the ratios to start working in my favorMy realtor provided me some provide private lending info who were able to offer NO refinance on property #2 but they could do a mortgage on a new property we were looking at for 20% down, & 10% interest.I did not have 20% ready to go as I was banking on the refinance for at least a portion of the funds and had to turn down the offer.Curious if anyone else has encountered these roadblocks and If I need to wait or if there is something I can do. 

We've discussed using other financing, cash-out refinances, hard money lenders, etc., but just can't bring ourselves to give the lenders all that money as the additional costs and higher rates involved in those types of loans makes the numbers seem worse, and stocks have been a better alternative for us recently than taking out expensive loans for more real estate. 

The 3 scenarios are as follows:Scenario #1: sell my condo and invest the capital gains in a market outside of California that I know well and has good cash flow.Scenario #2: refinance my condo under a conventional loan which would free up all of my VA entitlement.

@Russell Holmes, every deal is different and with each one you learn more and more so don't bet yourself up.  

These are things like:  talking to people,  getting over the fear of the phone, hard work , taking risks and betting it all, handling failure and rejection, perseverance, and picking yourself up off the floor, dusting yourself off and doing it all over again.

are you planning to rehab the property at all, or just refinance at the same value?