If it's from his personality, than only schooling (that works on his BRAINS not his FITNESS) will help. And that can take a very long, but both fun and frustrating, time.
If it's from his fitness, schooling to "get his brain" and less fitness work will help.
Sorry to say, but I have ponies into their mid-20's that act like high strung and very playful weanlings - even when they aren't fit. How did I get it toned down? A lot of consistent, slow & easy but brain engaging, work and being on my toes all the time around that pony so that any "high jinks" were caught and corrected right then before it got out of hand. When I wasn't mentally fit (too tired or strung out mentally from life) or physically fit (fever or stomach ailments) - I DID NOT HANDLE THAT PONY. Because, I simply wasn't up to it and I wouldn't catch the "little things" before the "hi-jinks" won out. Thankfully, I wasn't in "those" states very often!
Brain-engaging work - constant changes of direction while leading, lounging or ground driving. Constant up and down gait transitions - with enough practice that it is smooth and instantaneous, not jerky. Literally 1 stride walk, halt. 2 strides walk, halt. 1 stride walk, 1 stride trot, 1 stride walk, halt. Back - 2 steps - OOPS, not straight - step up to starting point and back 2 steps again. You have to do that in such a way that he doesn't think he's being corrected for being wrong (he's not) but just working to get it correct - the ideal/end product is the same, but the concept/thinking/attitude are different.
Two books that would probably help are Cherry Hill's exercises ones. The pattern work and gait work will actually continue to add to his fitness, but as his brain engages, he will think about what he is doing and his "playfulness" will be diverted to thinking and responding.
Honestly, this kind of work for showmanship and pleasure driving could take a while and you've already started late for this season. Took me 2 years to get a mare to "sort of" drive reliably and calmly enough to be out and about other drivers or in a ring. That was with at least 4 days a week of work (some of those were 3 -4 hours of driving/stopping/parking/driving - out on trails) AND 1 day of that work was with a pro trainer handling her or directing me in how to handle her (can't tell you how many times he stepped in to take over in the 1st 5 months!)... Literally, that trainer had me "quiet my hands", taking breaks to "quiet my mind" (he wasn't into yoga or meditating and that is NOT WHAT he called it, LOL), becoming more laid back and solid my own self... I NOTICED the work, change in attitude(s), in all areas of my personal life, let me tell you!!