I am not a friend of draw reins, so I wont address that idea.
Your horse dropping his inside shoulder on circles is either that he is unbalanced or is being evasive to work. In either case, I would pick up the inside rein and bend him TOWARD the inside of the circle and put your inside leg on and push him out. Even if he steps outward, off the circle it is ok. Just so he bend off the inside rein.
Are you riding in a curb , snaffle, direct or neck reining.?
If you are neck reining in a curb, it will be harder to effect only the inside rein and in which case you would focus more on using your inside leg. Be sure that YOU are not leaning into the circle when your horse does this. If you are leaning into the circle, your horse has no choice but to lean in also to stay under you. SO, when you apply your inside leg to push him, also take your outside leg off of him a little and really think of putting weight down into your OUTSIDE stirrup. You are inviting him to move into the weight and open area of the outside area. When he does step over and come off the inside shoulder give him a release on the rein and let him go forward, even if it's not on the circle. He did what you asked, right? Then go back into the circle again and see if you will need to do this all over again or not.
As for slowing the lope, you will need to settle your body down more, lean back a tad and breather out, think, "slow, slow, slow" with each outward breathe. REally think SLOW an heavy and your horse will slow.
If you need to use rein to slow him, take up the rein as tight as necessary but the instant he slows, even if it's not asmuch as you really want, release the pressure. Use lots of little "brakes" and realeasese over and over again, instead of holding (riding the brakes)