I agree, less bounce!
I'd try (if you have one) riding at a trot in a Western saddle, with a bit longer reins so you don't pull on his mouth as much. The Western will give you more of a 'supported' feel and that might help you when developing leg muscles and learning or bettering your post. Give him a loose rein, and keep your hands at the swell. Low and easy, just relax! Those English saddles can be a bit freaky feeling, to me it's barely a step away from bareback.
Push up with the horse, and rock back down with him. Get into the rhythm of him. I just about posted myself OUT of the saddle the first time I did it in about 7 years, so don't worry if you mess up! My mare too, has a pretty big trot.
As for leg strength, try to picture that you have a raw egg in each of your stirrups, and you can't, no matter WHAT, break that egg. If you break it, your too much in your stirrups. Same with the reins, if your hands move too far back, you break that egg.
What you can also do (my favorite way for the legs) is to stick a $5, $10, or when you get even better, $20 dollar bill in between your knee and the saddle. You MUST keep that bill firmly wedged in between you and the leather for say, 5, 10, 15, even 20 minuets...otherwise you don't get it! It's a fun way to 'reward' yourself for using your legs instead of standing in the stirrups.
Good luck, your boy is beautiful :)
EDIT: Sorry, I thought you where in an English saddle! XD I'd stay in the Western for a while longer to build legs and confidence (I feel safer in westerns, more stuff to hold on too!)
Wait! I'll fix it....