Unfortunately- there is no silver bullet to your answer, and it really comes down to how much do you want it and how important is it for you? 

Unfortunately, there’s no direct equivalent to a 1031 exchange for using sale proceeds to pay off another property.Regarding the 2 out of 5 year rule, it allows you to exclude up to $250,000 (or $500,000 for married couples) of capital gains on the sale of your primary residence if you've lived there for at least two of the last five years.

In some states however, you need to open the escrow account in the tenants name and unfortunately that is not possible at the moment.

Unfortunately most investors believe their excel spreadsheet will provide all the answers but I recommend combining your pro-forma with a greater emphasis on physical interaction with the properties and more importantly neighborhoods where you decide to invest.

If you brought your spouse and 2 kids with you, and you could argue all of your argue of your time on the trip was looking at real estate, and your personal business and activity circumstance defends being able to immediately deduct it and not treat it as a start up cost... likely 75% of much of the travel costs (airfare, food, etc) would be non-deductible. 

My next question is a simple one: through circumstance, we will almost certainly have real estate holdings in two states (Georgia and likely Pennsylvania).

It is unfortunately one of the biggest misconceptions amongst new investors and leads to unnecessary start up expenses.

Sorry, Unfortunately Voice to Text didn't work.First Point, is as a society we look at home ownership the wrong way, a personal residence is a liability vs buying investment property which is an asset. 

I have seen some sellers wait two years to close on a property those are definitely rare circumstances.

What you are describing is a fully thought out partnership or pre-arranged circumstance.