Flex Plate
You are trying to find something that doesn't exist.
I never saw any flex plates with a ring gear attached as you described for any LA small block. Also I have never saw a counter balance flex plate made by any other company then B&M. The counter weight pictured above is made by Quick Time.
The part your looking for must be custom made for a custom project. What are you trying to do as far as fitting what trans to a 360?
Here is a LA mopar to a powerglide. but you will have to use the Quick time balance plate with it for a 360