Ok so the way a curb bit works:
You neck rein left, your right rein becomes slightly shorter pulling back on the right shank. Assuming the bit has a solid mouth piece, the bit will rotate and push pressure onto the left bar. Having a slober bar will hold the two shanks together to that the rotation happens more easily. Seeing as with your bit when you neck rein left and your right rein is made shorter all it would do is cause the RIGHT side of the bit to rotate and all it would do is relieve any pressure on the right bar, not actually add any pressure to the left bar- a slober bar would make it so you get pressure on the left bar.
The problem with tom thumbs is that when you neck rein left your right rein is made shorter and the bit V's out and pushes pressure into the horse's tongue and RIGHT bar, giving them the wrong cue. A slober bar can help that on a TT, but not fix the tongue pressure problem.
I like your bit alot, but if it needs any more 'oomph' get a slober bar, curb straps simply amplify the pressure, because any pressure added to the bit now the bit has something to push against. It also applies pressure to the area under their chin. But again looking at your bit that doesn't seem to be what you need.
But PLEASE check your saddle it looks very far back on the horse and the horse's back is quite hollowed out because of it. It may be the angle of the picture though, do you have any more?