Downsides are it's normally 1% higher then conventional rates and is variable.

Trading up is a wonderful thing, but just to play devil's advocate, here is the major downside I see: When you "trade up" via 1031 exchange, you usually need to buy into the same market you sold into and do it under a time constraint.

The only downside with the HELOC is that the interest rate floats and we're currently in an increasing environment.

Based on cap rates in ABQ versus somewhere like Phoenix or Denver, your downside hope is that rents grow at a rate equal to inflation each year or more while in Phoenix/Denver your downside hope is that rents grow at least at inflation plus ~2% a year.  

The down side to a cash out refi would be that your closing costs would be higher. 

One down side is there is usually little appreciation but if you get a property that cash  flows on day one you will be set.

I will say it's not a bad downside scenario but if this is your base case, I'd pass.As for your question on how heavily COC is weighted...HIGHLY!

Using a heloc for a DP on a long term asset is essentially borrowing the downpayment on an ARM, easy to get over your head and under water on both the property purchased and the property you have the HELOC on especially when there is a high downside risk which is the current scenario.  

I wouldn't try the rental arbitrage without experience of managing tenants before.The downside of investing in another market is that it may be hard to find a good investor-realtor (not "investor-friendly" realtor) that will really help you find the deals to make money and grow your wealth.

The down side is that if your parents need to get another mortgage, this could inhibit them.