That's really the only thing that looks remotely like an error in your log? I would've expected to see more. How about increasing your instance size? One way you can have your R process killed without seeing anything in the log, is if the memory limit is exceeded--the OS will terminate the process unceremoniously.
If the leaflet map is being created before the application is responsive, then it is possible that shinyapps.io is seeing the application as not working and stopping it.
I would recommend taking the map creation out of the startup flow and see if that helps.
Yes, I’ve tested without the map and it works. I’ve seen flexdashboard example with interactive leaflet maps and tested their source codes and all worked.