I'm going to tell you something that you're probably not going to like: get off the horse and work those back muscles BEFORE you go out and buy a saddle.
I'm always astonished at how many people actually think that if they ride their horse, their back muscles will magically improve as well.
It's incredibly common to see well-conditioned horses with atrophied back muscles.
The reason back muscle improves is because it MOVES. If the horse can work the back muscle, the back muscle becomes stronger, becomes larger. On a horse with a weak back (even with a nicely fitting saddle), the horse is not going to be able to work the back muscle very much.
You need to get off until the horse's back muscle has improved enough to where your saddle is able to fit properly. You also need to realize that once the back muscle has improved, so STILL need to get off at least once a week and work that muscle to keep it in condition, or it will regress again.
Horses build muscle through trotting, and floating over ground poles is a wonderful way to build back muscle.
Get off and leave the saddle off. If you're competent enough to free lunge, that's the best way to do it. The lunge line messes with the horse's balance and can slow down your results. (Plus, isn't it nice to have your horse well-trained enough to respond to your commands without tugging on a rope?).
If you must use a lunge line, it's ok.
1) Make sure the horse can lunge properly. He should be balanced enough to keep a steady tempo around you. If he isn't well-balanced or can't keep an even tempo, you need to stick to trotting. Work both directions evenly. You want a nice working trot, no jogging, no speed trotting. (Though you should be able to control the speed at will. Jogging is nice for increased muscle control).
2) Once that's down, set down poles. Get him to do five walk poles. He should walk with his head down, back lifted, slightly stretching to get over the poles.
3) Once he can do those, set up trot poles. Set up three at first. For a horse, that's about 4 1/2ft apart at first, eventually working up to 5ft apart. I'd try 3 1/2ft at first, though do whatever distance your pony can do, just SLIGHTLY stretching for. You want him to keep up his even trot tempo. He should have his head lowered, back slightly raised when going over the poles. Eventually work your way up to 5 poles, spaced half a foot farther than you first started out with (so he has to almost prance to get over them cleanly). If he's tense, he isn't using his back properly.
3) Once he's got that down, go get yourself a milk crate or overturned bucket and set out three poles. Raise one side of each onto a bucket. Set them apart to whatever you originally started out with (3 1/2ft or whatever). He should go over them at an even tempo, calmly, head lowered, back raised. He should almost have to prance over them. That calm prancing really does wonders for the back. Eventually work your way up to 5 poles, spaced half a foot farther.
4) Once he's got that down, go to three poles and raise both sides. A 14.3hh horse can easily do 1ft high, so maybe try 8" or so for your pony. Set them apart to your original spacing. He should still prance through them, not jump. He should calmly go through them, head lowered, back raised. Eventually work up to 5 poles spaced half a foot farther apart. Once he can do that easily, he ought to be strong enough to go back into a saddle.
If you do this correctly, you'll probably find that you will need a new saddle. You'll find his balance improved, and he will probably work better for you. You'll need to do the free lungeing at least once a week to keep up with him.
If you do this properly, it will usually take a month or so.
I've had to do this on several horses and it's worked out well for me. I've spent several years working on it with my personal mare and even though she's been out of work for two years, she hasn't lost much back muscle.