Maybe the best bet is a rental refi on one of the two existing properties to be able to get a new home all cash?

There are definitely situations where selling to a wholesaler is someone's bets option, but they're the exception, not the rule.

I'd be willing to bet most of the tenant problems people post on BP about are when they make an exception to their screening criteria. 

I bet you can find your answers in the city of Chicago tenant's law and regulations@Carlos Valencia @Albert Bui

Your best bet is getting the heir to agree to sell.

He bought it in 2021 so I bet it's low.

If you already have a pre approval for FHA then starting locally with a house hack is going to be your best bet.

Getting a local realtor to give you and ARV would the best bet but you can use sites such as Redfin (be careful of Zillow's Zestimate) to get you in the ballpark. 

Who wants to bet it's 6%?

I bet there are options available to you such as using a "buy before you sell" (orchard, homelight, homeward, etc.) bridge-loan type program, or you may be able to use a HELOC or other bridge financing.