After doing some simple math (MB says a 2020 2x4 Sprinter 2500 high roof cargo van is 107.5 inches tall and you're saying the Winegard is 13.5" tall), I'd estimate the height of your Interstate 19 with the dish to be roughly 10' 1". However, if it were me, I'd build the garage with 11' of interior height just to make sure there's no issue with garage door openers, or anything else.
That said, these numbers are purely a SWAG, and if I were building something, I'd measure twice and build once to make darn sure the height numbers were right before I broke ground.
Oh and something fun to consider, which was my brother's idea: once you have that Winegard up there, have someone air brush with non-metallic paint so it looks like you have a minion on your roof. Maybe Bob.