I don't want this to sound rude, but I don't know how else to say it. 

the property’s rehabilitation is scheduled for completion in 2025 and the rent will subsequently increase, can I proceed with a cash-out refinance based on the current rent roll?

It's doesn't really sound like you are much into being landlords so doing a 1031 might just change from "annoying when things come up" to full fledged head aches when you buy more and or larger properties in your current market.

Your issue more so is the seasoning period for the refinance is what it sounds like.

Several factors at play: the sales market has been slow so many would-be sellers are converting houses they can’t sell to rentals, lots of new construction units have been completed recently, and in-migration has slowed down a bit.

Sounds like you’re juggling a lot.

Completely agree that each market is unique, and success comes from actually doing the work.

It sounds like that you have been getting ready for awhile.

They don't care when you try to explain all the future projects, they actually hate hearing that since it sounds like a scam, when an investor says, "Give me a good price and I will have a lot of work for you" it sends chills up their spines. 

The idea of debt-free is that if a person is going to retire and has to completely depend on the income, they don't want a severe recession surprising them and causing them to default on the debt and losing the properties.In a normal world, I would do that as well.