@Tobias Joneses, The time lines can be daunting.  But if it encourages you we're seeing a 200% increase in 1031s just this year.  and the fail rate hasn't increased a bit.  Planning is important of course.  Finding the new property and getting it under contract even before you list or sell your old property can help - You can stagger the contracts either way.  But you must close your sale before closing your purchase.  

So get the hard part done first - find your replacement and then sell your old property.

Regarding the zero sum game - if it truly is then do not sell. You're just wasting commissions and closing costs. But there are many reasons to still sell that can make it worth your while and increase your ROI at the same time including

1. Accessing 100% of equity to purchase new property at lower interest rates with fixed term financing as a hedge against financing.

2. Going from a higher capital repair potential to a building in better shape at lower risk for cap ex.

3. Changing sector - residential to commercial or multi family.  

3. going from something with HOA to non-hoa.

4. selling in a topped out market and buying in path of progress

5 1031ing into something you might like to live in a couple years time.  Then selling your old primary tax free and moving into the property with deferred tax so that it stays deferred while the sale of your primary is tax free.