Avi Reichman I would advise to connect with a Broker or Real Estate Agent here on BP from your state or your local area.

By putting your rental on MLS, it will be marketed to brokers who are incentivized to find someone qualified to fill the vacancy.If you'd like to handle that on your own, you can certainly use Zillow and get plenty of traffic there as well.

Any recommendations for 1) brokers who could do the BPO (ideally I bring the broker to ensure Independence); and 2) an Illinois lawyer who will know the mechanics of setting this up?

They're not brokers but most claim to be direct to seller or one away from the seller. 

As a list broker I know that people  will definitely call to complain if they have the feeling that you are in with Big Brother (maybe you're too young to get that reference)You might talk about this the same way you would with almost any audience: home ownership can be a big responsibility with the expense and maintenance....

How to ensure Listing Agent presents your offer to the seller.In advance of even looking at a listed property:1. email or have your buyer's agent email your Approval Letter for your MAX purchase price, regardless of h...

Try to find an insurance broker to shop around for you. 

After these preliminary steps https://www.biggerpockets.com/forums/552/topics/562694-fl-mortgage-broker-ensure-listing-agent-presents-offer-to-seller  1. 

According to the broker, no environmental issues that she knows of.

Commercial brokers such as myself have a network of buyers lined up ready to pounce when smart sellers put the feelers out.