The trainer at my gym wants me to do more sets with a higher number and also wants me to spend more time on the cardio equipment. Would that work better for me?

I'm sure that your trainer means well with these suggestions. In fact, I'm sure that you're being told exactly what they were taught in their certification course. What this program has shared with you is not the same as the mainstream recommendations in most gyms and muscle magazines. However, we will say that the research clearly supports the methods that we teach you in this program. And with it, you will maximize your benefits while minimizing the time required. That's a win-win, so give it a shot.