Calculating a figure for "cash for keys" offer

[Paul Witte]

I am in the due diligence period of property--a duplex to use as a buy and hold rental--with closing scheduled on 9/30.  The biggest issue I'm struggling with is a tenant who has been in one unit since March and is $2400 (2.5 months) behind on rent, and has had multiple noise/filth complaints.  Obviously I can't evict him now, and even after January 1st, the process will be so backed up that it will be months before I can remove him.

Part of my issue will be the lost rent and piling up expenses, but maybe a bigger issue is my strategy here. I was hoping to make this a BRRRR. I am buying for cash at 40k below market value in as-is condition, and after putting in 15 or 20k, hoping to increase the value significantly more. My plan has been to do a cash-out refinance after a 6 month "seasoning" period (necessary, I've been told) to pull most of my capital back out and do it again. But with a non-paying tenant who might still be there by then, I doubt I'll be able to find a lender to go along with that with such a poorly-performing property.  I figure I have to assume a worst-case scenario--6 months at $925/mo = $5550.  PLUS, the lost opportunity to get my capital out and get another deal, perhaps one of the foreclosures many people are expecting to be more prevalent in 2021.  

So in your opinion, how much is a reasonable offer?  I haven't seen any discussions of paying-your-tenant-to-leave deal analysis!  How do I think through this?