I would actually recommend against doing what you're suggesting. In effect, you want to broker a deal between two parties, acting as the channel. This is similar to Amazon's affiliate program, I believe. Is this a correct description?
First off, if you're trying to bring liability issues closer to you, you should probably plan on being a big organization. I say this because you will need plenty of attorneys, and a serious anti-fraud department. It's a lot of overhead -- Paypal spends a ton on this kind of thing. Are you sure your company can handle that kind of responsibility? After all, if doing anti-fraud isn't your core competency, it's a difficult and dangerous field to dabble in...
It's not a good idea to allow customers to transfer money between each other. They trust you, but you should not assume that they can trust each other (WRT bank account information, the only way I can think of to directly transfer money between them). Plus, it might take too long for the money to clear.
I would recommend that your company (Org X) accept the credit information from Z. Then on a monthly / by request basis, you pay Company Y. You can take your fees directly from the info from Z; you can "handle liability issues more directly", and it's a pattern that's been done before (amazon affiliates, ebay, etc.) Also, it fits it more with the structure of the payment industry, rather than trying to force a new model (X->Z transaction combined with Y->Z transaction is just a little odd).