You want to keep (roughly) the same amount of debt and just swap that out for new debt at better terms. 

You need to know all the options available to you: you can keep it as your source of monthly cash flow, or you can swap it for another property (known as a “1031 exchange”).

Is there a way to set this up without selling each property, but using some sort of direct swap?

@Eric James, may be right and he's thinking a swap would eliminate the tax on the sale of the rental. 

Or finish swapping out garbage disposers. 

I would start looking for Facebook groups dedicated to the topic and go even further and look for local groups in the cities in which you are interested in and join them for discussion.We have a few here in the Orlando area (central Florida Airbnb, Airbnb thought counsel, etc) there are swap groups for owners to trade housing.

@Eric Fung   Its not uncommon that just swap the outlets without running the ground wire EXCEPT in the kitchen and baths where you do run the ground and install GFI outlets per most places code.Your area's code may require the ground wires in bedrooms/hallways (the remaining outlets).   

They will try to convince you to swap your Title back and forth so they can sell you a loan, but that's a bad idea for your LLC.

Or, the payment amounts are swapped. 

If you want to swap PM's down the line, you can.