Can I do this with a 1031 exchange?

[Heather King]

I will be closing on an out of state rental property at the end of the month. I am interested in executing a 1031 exchange. My question is this:

Will a 1031 exchange allow me to pay off my current primary residence if it is converted into a rental/investment property within the 180 day window? Meaning, I would:
   ~close on rental property at 123 Main Street
   ~take profits from 123 Main & 1031 Exchange them by paying off current primary residence at 567 Oak Street
   ~take out new conventional loan and move into new primary residence at 9876 Eagle Ave
   ~rent out 567 Oak Street
   ~complete all tasks within 180 days

I hope that makes sense. Any advice would be greatly appreciated.