Movies in iTunes not playing continuously to Apple TV 4th Gen

I've been adding/converting movies I've purchased on DVD to iTunes for years. I stepped this process up once I learned that the 4th generation Apple TV was coming out.

Now that I have one hardwired to my home network, I'm finding that I have to babysit the Apple TV as it will NOT play any of the movies I have in iTunes continuously. In other words, the movie (any movie) stops playing altogether or the sound continues and the video stops, and I have to back up about 20 seconds and wait for everything to load again. This happens multiple times per movie.

My 'host' hardware is a iMac (20-inch, Early 2009) 2.66 GHz Intel Core 2 Duo with 8Gb of RAM (maxed). Running EL Capitan 10.11.2 Beta (15C47a) with iTunes 12.3.1. Network is at 1Gb (except for the Apple TV which is only at 100Mb). I have not tried connecting via wifi as my wifi is only n (i.e. not ac which the Apple TV has) because I figure it will be a slower connection.

iTunes resides on a dedicated 6TB external firewire (800) drive with 1.31TB of free space (as of this writing). The drive was last optimized about two months ago.

I figure that the problem isn't the Apple TV, but iTunes as it seems to love to give me the spinning beachball whenever I want to do anything such as check for App updates.