Hello. I am not sure about my further answer and we can't know everything about your rig from gif's and explanation. Nevertheless: I think, that the problem appears because of the multiple constraints (nested), which does not work in Spine. First constraint is your path constraint and the second is transform constraint. It might be not obvious, like two nested transform constraints, but I think it might be it.
Anyway, I can suggest you to achieve the same result with easier way.
You can use only 1 bone (your "main bone") to control the deformation of the string and the bow itself. To achieve that, you simply need to adjust the weights on the path's correctly. Those points on string path, that you want to bend the most - must have 100% weight of your main bone. And those, points, which need to bend less - must have less % weight (in your particular situation 33% of the "main bone", other 77% can be set to something static, for example the bone that contains all other bones of this bow). Look at my gif example below. You can see that in my example the top and bot bones are moving with the path, yet slower, than center bones.
Hope that helps. π