Advice Needed: International Work Assignment - NOLA Home Decision

TL;DR: asking advice from the internet on what to do with our NOLA home while on an international assignment in the Middle East for 4 years.

My wife and I (and our toddler son) have been lucky enough to have been chosen for an international assignment with our company in the middle east (Oman). We'd move at the end of the year for a 4 year assignment. We own a home in Uptown NOLA (purchased in 2009) and are trying to figure out what to do with it.

Purchase price ~$400k; current conservatively estimated value is between $650-750k. Outstanding mortgage balance is $380k after refinancing 3 years ago to extract equity for some needed improvements.

An important consideration is that we're unlikely to return to NOLA after these 4 years -- maybe only a 10-15% chance. More likely scenario is that we'll pickup another assignment somewhere else, or relocate back to NOLA and then immediately to Houston within a month or so (Oil & Gas employer).

We've evaluated our options as follows:

Option 1 -- Sell the home.
Option 2 -- Pickle the home
Option 3 -- Short Term Rental (AirBnB)
Option 4 -- Long-Term Rental (Yearly tenant)

Originally we leaned Option 3, as we like the idea of having a home to come back to when we visit each year, or in case there's a geo-political reason we must return (e.g., war with Iran). But after giving it some thought and thinking about the financials, I can't get over the idea that prices in NOLA are high, with low interest rates, and, because we won't have been using it as our primary residence for 2 years (over the 4-5), we would be dealing with taxation of the capital gains when we do eventually sell….this is making us seriously consider option 1.

What say the sages of Money Talk?

Please let me know if you need more information. Happy to provide.