I've been looking at your product and I'm very interested in it, but I was wondering if there's a way to make specific fields in specific tables different.

To be specific, I would like to share both Kunena and JomSocial with all of my slave sites with a slight modification. Some of the forums sections in Kunena, I would like to be unpublished in one slave and published in the other. Likewise, I'd like some JomSocial profiles fields to be required at registration for one, but not required in the other.

Is there a way to do this?

NO.
When you share an extension, this use MySQL facilities to share the MySQL table(s).
So that share all the records and all the columns (fields).