Now I am trying to decide to sell (take the long term cap gains hit) versus a 1031 exchange (never done one) or just relist it. 

How long is your redemption period in SC? 

And even then as long as the tenant pays something I don't file for the eviction.

@Ray T.I’m actually on an overseas assignment now in London, but my long term residence is in Phoenixville.

@Shrikant KakaniColumbus, OH is one of few markets that have property with enough cashflow to pay itself and all the metrics for long term appreciation. 

What are the top amenities in the area for the high performing STRs?

As long as you give the proper notice to the tenants, you should be fine. 

Current lease term (expiration date, month-to-month)7.

Presumably my gain will be much (less) on the second sell transaction in CA.Are there any regulations on how long I must hold my 'new' CA property before selling it (and going out of state) to avoid CA taxes on first transaction? 

I would be wary of buying a home in a residential neighborhood in ABQ with the goal of having a STR: Only CA rivals NM in terms of economic governmental tampering.