I am never one to let a source system architecture drive an analytical solution.

It sounds as if more work would need to be done on the dimensions than anything else. It is ok to have multiple hierarchies in a dimension--especially a product dimension. The first thing I would do is analyze the product map, see how clean it is, and proceed from there.

Like Paul says, however, it is not uncommon for a new system to introduce new potential facts--just make sure the are ITEMS OF NEW BUSINESS VALUE.