re the bareback pad, it depends on the shape of the horse. And the material the pad is made of.
NEVER EVER EVER buy a bareback pad that has stirrups. Those are just plain dangerous, and have the added nasty side effect of putting ALL your weight on a very narrow band across the poor horse's back.
My gelding's backbone sticks up a little bit. He is 17 and very long-backed, with awkward hindquarter conformation, so it's hard to get him using his back. Even though he is very fat at the moment, his backbone still sticks up. I do ride him bareback but never for long because his backbone literally rubs me raw in very uncomfortable places if I stay on for too long. A bareback pad is awesome in that situation - I like two saddle pads with shaped toplines (straight/flat toplines will slip backwards) girthed on with either a roller if you have one or stirrup leathers.
Once, I didn't even bother girthing the saddle pad I was using (only one because the pony I was on was comfortable to ride bareback so I didn't need the padding). Pony shied 3 feet sideways. I didn't slide sideways at all and stayed with him so easy - wouldn't have been able to stick on straight bareback. But, and this is an important but, that was the ONLY saddle pad that didn't slip on the other horse I had at the time... so it had awesome grip.
You can get non-slip bareback pads. Much better than the sheepskin ones, I have found sheepskin to be horrible on anything but a horse with a high enough wither to hold the saddle steady even with a very very loose (or broken!) girth. Shaped ones are better, as in shaped to allow for the curve of the back and the horse's wither, because non-shaped will slip.
Regarding encouraging the lazy horse to move forward, DO NOT do too many circles. Circles slow down a horse. They are great for the horse that is too forward/excitable, but will make a lazy slug worse. If you go point to point with purpose and direction, and do something interesting when you get there, you will encourage your horse to be more forward.
I used to have a very very lazy pony. Had to whip him hard with a dressage whip to get him into a trot, and then again every few strides to keep him in it. Guess what I did... I asked as softly as I could, then harder, then harder, then made him pay for ignoring me. I kept it consistent and eventually, as long as I had a whip, I could put him into a trot and pretty much forget about him. Canter was harder because he bucked as well as being a lazy ******* but I learned to ride out the bucks (giving him what-for every time he tried it on!) and keep him going.
The most important thing with a lazy horse is to NEVER punish the forward. If you're asking for a trot and it takes a massive effort to get the horse to break out of the walk, and it goes into a canter, that's ok. Let it canter for a few strides, then calmly bring it back to a trot.
My gelding decided to try on the "I'mma ignore you" the other day. Luckily for me I'd decided to ride with a dressage whip. He is 17 and very educated, and I know he KNOWS he has to move forward off a light aid. I gave him ONE chance, which he ignored, then I flicked him with the whip. He grunted, pigrooted, and broke straight into a canter. That was ok because I'd asked him to move forward faster than a walk. So what if he went a bit quicker than I asked him to? I let him go for 10-ish strides, then asked him to come back to a trot, then a walk. Asked for the trot again and he was lovely.
Funnily enough yesterday I got on and he was back to his lovely responsive self.