Gates? If applying for a job in the industry, be sure to spell basic terms correctly. Details count! I was at first thinking you meant that all the jumps would be gates...took me a while to realize you meant gaits.
Target your resume to what the job will be. If you are applying to a few different places, with some being more hunter, some jumper, and some dressage, then customize the video to focus on that discipline. Don't be boring and show too much of the other stuff. Keep it short, and make a longer video available if asked for.
If your potential job is bringing along young horses, try to include a schooling ride on a young horse in your video. May not come across as impressive, but it would be more relevant that watching you jump 4' on a school horse.
The big barns are looking for great workers and won't probably care too much of achievements on school horses, unless you are the one who trained them or have some show footage...or have a very impressive demo... Anyway, they'll see if you can ride but they'll teach you their way of doing so...
I don't know you so I can't assume anything but a 3' course is a hell lot of a difference than a 4' one, IMHO.
And showing lateral movements is not that easy either...
I suggest you do a dressage test of your level than add little extras of movements you can do really good.
Then a perfect hunter course followed by a jumper one!
Short sweet perfect!