What a cutie! Your boy looks great in English tack! And you have very nice posture.
Did you have your girth running through the loops at the bottom of the yellow pad? Does the pad also have straps about mid-way up each side? If so, these wrap around the front of your saddle and you slide the first billet through them (or velcro them on, depending on the pad). This will help your pad from sliding back under the saddle.
As for the whole saddle sliding back, does it fit him correctly? Has he always needed a breastcollar with Western saddles? If so, he'll probably just need one for English too, just because of his conformation. In the English world, you'll find they're called Breastplates. A Martingale is a whole other ballgame and is not an item used to hold the saddle in place.
As for bits, I would recommend a French Link or Oval Mouth bit with either loose rings, eggbutt, D-ring, or full cheek. The double-jointed bits are much nicer on your horse's mouth when you take up more contact. They're less likely to basically fold in half like a regular snaffle and hit the roof of your horse's mouth. What did you dislike about the O-ring snaffle that you tried? Do you think your horse needs a harsh, twisted-mouth bit?
Everyone else gave you some good tips as well. One additional thing for your girth search...elastic on BOTH ends is better than just one end, IMO. As your horse moves, he'll have equal pressure and release on both sides. If you're only able to find a one-sided elastic girth (they're much more common), then I'd actually recommend rotating it from day to day so that you have the elastic on opposite sides. I find that keeping everything in a horse's training symmetrical, leads to a more balanced horse.
Oh! One more thing: English riders think helmets are cool.