Good Grief I have to suggest that if your trainer had to 'lighten' a horse by using a twisted snaffle then they are not the sort of trainer you would want within a hundred miles of a horse. Same deal with the use of spurs. A horse can feel a fly land on him so IMHO no horse ever needed spurs.
It shouldn't matter whether you ride with a bit or not to how your horse goes. Personally I ride my horses in a cross under bridle (no bit). This included a huge Tb who was very forward moving and loved to move out and my little Ausie stock horse, (nick named the Pocket Rocket on the CTR circuit).
They both went/go fabulously well in this bridle (I no longer have the big chap - hence the past tense)
They both went beautifully in a Myler snaffle as well but I like the bitless approach because, as someone mentioned for the long ride, I like the idea that my horse can easily snatch and graze as we go.
If your horse is "fingertip light" with the "heavier gear", that's what you ought to be using. If he is light on that gear it will not be uncomfortable for him. He obviously knows what he can get away with, and when. You may be able to transition back to "lighter" gear once you have a handle on him and both of you have your communication issues sorted out.
Contrary to some opinions, a properly adjusted bit in the horse's mouth is not uncomfortable and the horse can easily eat around it. The bit only gets uncomfortable when the horse resists it, regardless of how aggressive the bit may appear. When a horse resists the bit, it should
cause some discomfort. If the horse's mouth has become so hard that it is no longer responsive to the bit, a twisted wire snaffle will remind him of his manners fairly quickly, causing him to resist less, and thereby helping soften his mouth once again. Once the horse is responsive to the harsher bit, he can be transitioned back to the less aggressive bit.
Many trainers will "lighten-up" a horse who is heavy on the bit by going to a thinner snaffle or a twisted wire snaffle. There is nothing wrong in that. Your horse needs it.
I am a proponent of spurs for training. I find horses respond quicker, more eagerly, and are more willing and obedient when I train with spurs. They learn faster. This eventually translates into a submissive, obedient, safe, and happy horse, which comes with the added benefit making a happy rider. I don't always ride with them, but I train with them.
Just because you wear spurs doesn't mean you are cruel with them, and the fact that you use an aggressive bit doesn't mean you are causing injury to the horse. Someone, at some point, must teach your horse discipline. That involves causing some level of discomfort for disobedience. If you can ride without doing that, then someone else has done it for you and you can thank your trainer...though he/she may be more than a hundred miles away.