Hello,
quite some time has passed since you have posted this question, have you solved this problem about multi channel attribution?
I worked on a project about that, and we used markov chains to model the path of a customer to conversion. The contribution of every channel was derived using a "removal effect": for channel X we computed the drop in conversion probability from the full model to a model where channel X was considered as an ending state. Comparing the drops of all channels we got the contribution of each of them.
How have you solved your problem?
Regards
Marco