Another Galloway fan here - I too dropped a ton of time from my PRs by switching to his run/walk. And here is the part some people have a hard time with .... I run 30 SECONDS and Walk 30 SECONDS!!! I am sooooo much faster using this interval than I was with longer ones.

So I don't care what anyone thinks. I view like when someone comments if I have a sweater on and they think it is warm - know what I'm not making YOU put a sweater on, so why do you care?
For some reason, this 30/30 interval makes my 50 year old body happiest. I want to keep racing as long as possible, so I am doing what makes my body happy. I was astonished at how well it is working....no more flair ups of bursitis in my hips, no aching knees or back - just a good tired after a race.
Obviously, YMMV, but I cut almost 8 minutes off my half time and and 6 minutes off my 5k times. And to top it off, these races were in 80 degree heat. I can't wait to see what I can do when the temps get into the 60s and below in the Fall.
I thought I might be embarrassed doing such short intervals in a race, but the truth is once you are in a race, no one is paying any attention to you cause they are too busy running on their own plan.
Don't look at your times now - you are early in the game and you will improve. Just keep working to find what makes you feel best. While I'm sure your coach is a lovely person don't compare your performance to hers or to anyone elses!!! Some folks have a natural ability for running and when they work at it, their times reflect it. Others, like your truly, will always be "hackers" to borrow the golf term. We love what we are doing, but are never going to be terrific. Cut yourself some slack.
Good luck