The bit you are using is an excellent bit, especially for a horse that needs some reinforcement around the turns.
You haven't mentioned any reasons you feel this bit isn't suited to you and your horse....? I.e. Evasion of the bit, throwing of the head etc etc. The issues you are having under saddle will be corrected with a stronger seat and leg, the bit won't do this for you. A bit won't 'back up' your leg, if you really want to back up your leg try a crop.
The other bits you posted are very good general purpose bits also, but I wouldn't expect to see much of a difference in the way your horse behaves as a result of switching to one of these bits. The french link will be easier on the roof of his mouth and may encourage him to work a little softer however you will lose the steering power provided by the full cheek you currently have. Trial and error, see what works!
I would work on leg and seat aids before I rushed out and changed bits personally.
All horses deserve, at least once in their lives, to be loved by a little girl.