Recent updates of Exchange will not change your options here. Microsoft has modified how public folders work in 2013 and there are improvements, but remote and mobile access to them has not gotten easier. I've found it's more difficult to access shared folders in Exchange 2013 OWA than in 2007's web interface. For mobile, it's still just as unpleasant.
You've already identified the two main solutions people are using these days:
- setting up a separate mailbox to share between users
- using CodeTwo or similar software
I've also seen Exchange admins set up the shared mailbox, but then augment that with apps installed on the smartphones that make it easier for users to interact with what they're storing and sharing. I like that route, but any decision about which apps are best to use are going to be very dependent on your userbase and what they feel comfortable with. Many of these apps have free trial periods, and I recommend taking advantage of that.
For the sake of completeness, I should add that calendar publishing is an option that works well enough with iPhones. This method is insecure. It's a good if your shared calendar is only used to track public, promoted events. It is useless if you want to restrict some of your Exchange users from seeing the data.