If you used
self_contained = FALSE, you should have a smaller html file because some of the stuff are into folders. But even in this case the loading time could be heavy because everything loads in client side.
To minimize the loading time, you could have an approach of client/server when you load data in the server when needed to print a plot and render the plot on the server to send to the client. I think the app will have a smaller loading time but you will have (small ?) computation more often.
Also, with this approach, you can have some menu for user to choose which data to look at, and instead of having 60 graph, you may have less. For example, it seems you have 5 tabs. I assume each tab have the same graphs but different data here. If you replace the tabs, by a drop-down menu to select what to see, you can have a one page dashboard with 12 graphs and change the underlying data when needed to rerender the 12 graphs. All this is achievable using shiny, on its own or into Flexdashboard
Just some ideas I wanted to share - Hopes it helps