Can you work more at the working walk on contact to engage his rear then slowly loosen tne reins so he doesn’t lose the engagement? He might be a hair short in the step department and not be stepping up and under enough to get that come from behind walk and jog.
You want fewer bigger steps, not more smaller ones, that will give you the stretch and relaxation. If he can conformationally do it, hip and shoulder angles may not make it easy for him. Had great luck loosening them up walking them over ground poles, those help with straightness too. Does he track up straight or trail a hip in or out? Easy to see, have somebody stand behind while you ride away in a straight line. Or rake the ground smooth and ride him in a straight line then hop off and look at the hoof prints. Back should print right on top ir slightly ahead of the front. If it prints behind, he’s not reachng up and under to properly push off. If he’s not in line but crooked, he’s not going to be able to properly engage.
Also, at 16 he is going to be experiencing some arthritic changes. Would be a good time to look at his joints behind, especially hocks. Hocks generate that push off when they are properly engaged. If they are stiff or sore they can’t step up to push off and often go crooked to protect the joint. Body work can help with stiffness but it’s totally unregulated , you need a vet to take a look at those aging joints anyway.
He may just not ever be very good at extending his stride due to conformation but you can certainly improve where you are now. It’s a new thing, be patient and make sure he can comfortably do what you are asking before drilling it extensively.
ETA he might also just not know he can move forward more freely, most tend to go too slow and constantly correct and slow if the horse makes at extending stride. Think about that too, he might be assuming he’ll get pulled up for taking bigger steps if most of his riders over the last 15 years or so checked him up for stepping out. Step out more at ALL gaits, let him extend, then collect keeping the impulsion.