Here’s an idea, expand on the in-game challenge menu with some sort of community building features such as rating challenges that you’ve played and leaving comments which people can read.
Have a weekly and monthly top rated challenge so that people can have a look at which challenges are interesting to look at every week
Have tags on challenges which you can use to sort or group fleet types for easier browsing
Have a mini-window showing the deployment silhouettes to give you an idea of what the challenge contains
Have some kind of tournament where people can submit their best fleet in a tournament, a server runs a few simulations and then a resulting video / simulation would be sent back to you to see how well you did. Tournament winner gets Gratuitous Bragging Rights TM.
Hall of fame for previous tournament winners and let you view their fleets for all time.
Also some kind of messenger system or a profile page where people can view your ranking / fleet designs / personal message / leave comments on your profile page (and also a way to block messages from people XD)