You should try "bumping" him off your reins. Give very slight calf pressure , and if he breaks into a trot, confer a firm, but quick, pull on your reins, which i call bumping. If he does slow, compliment him. A couple steps later repeat the process, and if he trots, bump on your reins. Over time, he'll learn to waddle at the speed you want him to. It's always worked with me!
Answers: A horse should have different cues for pace, trot, and canter, asking him to speed up at any gait shouldn't cause him to switch to a higher gait without you asking for it. My horse does singing cues, if he's at a walk and I keep clucking at him, he keep walking faster and faster unless I say "trot", and he'll go from a very slow run to a very fast trot if I hang on to clucking until I say "lope". The horse my sister rides uses leg cues, but he has a different cue for each gait too. Try asking him to speed up while applying slight pressure to the rear on the reins, maybe he'll get the idea to speed up, in recent times not that much.
gather your reins and apply LIGHT leg pressure and drop the reins to a comfortable length, then sit forward a short time more in the saddle making your body language tell the horse that you would similar to to go a little faster. this works on my horse.
You need to get hold of his attention first, wiggle your reins a little, and squeeze your legs against his sides, and you may need to try spurs. You may even inevitability to have him "rounded" up, ask your trainer about it. It also helps your horses go together and gets them "up"