BTDT with a regular and wonderful clinician we had at my old barn. Learned never to do a 2 day clinic with her - but got a lot out of 1 days, and gave the horse the day off afterward.
I see 2 independent questions in your post. How to warm up, and how concerned to be about the soreness. With the caveat that I warm my current horse up the way you described you usually do, it sounds like the horse went beautifully in the lesson, so it might be worth trying this system out to see if it’s what he likes.
I wouldn’t attribute the soreness to the warmup, but to the amount of work you did in the lesson. If he doesn’t have the muscling, you have to do less / take more breaks, etc, but that’s not to say don’t do the work. Just do an appropriate amount for his fitness level, which you know better than a clinician.
Not sure based on what you described that I’d throw the baby out with the bathwater.