Does anyone have any experience with this that can provide some insight on how to structure a deal? 

He will be providing the capital to cover the closing costs and part of the rehab.

Addendum states: - Buyer to provide financing for 70%. $225 X 70% =$157,500.

There shouldn't be any need to negotiate them as you would negotiate rent, they just are what they are, and the owner is required to provide proof of those costs to you.

Can someone provide me with some financing ideas other than the two that I just mentioned that would enable the other heir to receive cash from their portion of the equity based on its current assessed value and allow me to take ownership of the home, subsequently remodel it, and rent it?

Based off the numbers I provided above, how much could I get out?

I have house hacked 3 times in the Logan Square & bucktown neighborhoods.It will probably easier if you can provide some more details on the analysis....maybe consider BiggerPockets calculator. 

Based on the new information provided by the City for what can Qualify; I would say this likely could Qualify for an Express Permit.

And they don't provide much info on dividend distribution. 

I would recommend you read the book 'ninja selling,' as it provides you with a solid plan and schedule filled with action items to follow and execute to get results (if you follow it) And its not cringey, salesman strategies.