Kind of...I know it's been 6 months but I'm back on this project.
Essentially what I had to do was re-think how I wanted my users to access information.
Now, instead of letting the groups look at each other's profiles, I set up searchable user lists with only the information I thought group A would want to see of Group B.
And then I killed the access of profiles (except by the user).
Additionally, Group B, as the business model dictates, will be limited to a specific number of users and require that website admin set up their profile. In this way, site admin can set the correct access level for those users (which is key to the data presented in the user list).
It's not as great as I would like it but it's free and it seems to do the trick...for now! Perhaps in the future I will consider purchasing the services of a good code person or incorporating commercial plug-ins.