Profiling the app in the browser might help. I have a largish app that uses navbarPage and the page build speed was getting slow. Using profiling in Chrome (developer tools) identified the 'culprit'. A fix/improvement is in the works https://github.com/rstudio/shiny/issues/381#issuecomment-33750794
Run the profiler from a code window in your app. Using the shinyAce package (https://github.com/trestletech/shinyAce) I can edit (and run) code, including profilers from within the app (i.e., call reactives etc.). See link below (R > Code). Note that code evaluation is deactivated on the server but the source code for the app is on github if you want to try this out (see About page)
Write your code in regular R functions that are called by reactive functions. I am in the process of rewriting my app so that it can use knitr for 'reproducible research' (R > Report). This restructuring makes it easier to use profiling libraries from R(studio) without starting the app.
Rselenium is an R interface to Selenium, testing tools for web-apps (https://github.com/johndharrison/RSelenium). I have only just started using this but you perhaps you could use this with something like system.time to compare speeds for different components.