The self-manager isn't paying a property manager, but if the self-manager is leaving out the "managing" part, then almost certainly (s)he is giving up lost revenues that far exceed paying someone to actually manage the property.Managing means you are responding promptly to all inquiries, monitoring rates and comps daily and making adjustments as necessary, ensuring that the property is safe and clean, that everything is operational, and quick responses and resolutions when something goes haywire.  

If you're a high earner, say $500k/year but can live off say $100k/year, then you can do it quicker.

If you are using DSCR refinancing, you can refinance quicker than 6 months.

He has promised countless times over several months (5 months to be exact) to come back to us with "a proposal by the end of this week" via email on 11/28/23 and "we will get this wrapped up this week" via email on 12/11/23 - and we are already in the first week of February 2024 without a proposal and without any progress in coming to a resolution.

It's true saving for your 1st property will be quicker if you save in cash, in a bank or some secured asset class with no fees.

Find a peaceful resolution. 

Is there any other way to have him out quicker?

@Jide Alufa scale quicker with multi-family!

I suppose you can do delayed financing as well if you want to close all cash to make it a quicker transaction. 

With this in mind, should I do a cash out refi on the property in order to buy another property now or should I try to pay it off quicker and add equity, or do nothing at all?