I’m looking for a solution that would allow form submissions to be submitted and approved/denied for automatic inclusion in either a searchable table or geodirectory. Is that possible with a Gravity Forms addon?
You can use Gravity Forms to collect and store your date. Then, you can use GravityView to create your directory.
They have an approval feature for the entries built in:
The entry needs to be approved before it can be shown in your directory. I recommend reaching out to them if you need assistance with their plugin, or any questions about the functionality. That is the absolute best way to display Gravity Forms entries.