
One rule of thumb I have with my puppies when learning to move on the lead: teach them to walk before you teach them to run.
I wouldn't focus on gaiting your puppy at all right now. Just get him used to walking on the lead and reward him when he's walking beside you without his nose to the ground. Once he knows what you expect from him when walking, then start moving him faster. Short training sessions are good, but you want to be doing them multiple times a day. I tend to do 4-5 training sessions over the course of the day, each lasting no more than a few minutes each. Get what you want, then reward and end on a good note, then go back and do it again later.
I'm not sure what breed you have, but I show gundogs and always have food with me in the ring. I don't throw it and I'm not constantly feeding my dog, but my dog does work in anticipation of a potential reward. All I have to do is reach for my pocket and her tail starts going a million miles an hour. There are plenty of ways to use food in the ring without being disrespectful to other exhibitors, so why not do it if it helps your dog enjoy showing?