I got the copy.asmx to work to copy a file from one library to another. This doesn't seem to work though with destination library having a content type set with required fields. I set up source library to have same fields but no luck. Even tried setting up source library to have same content type.
Since the destination library is dynamic (multiple libraries available) I use a lookup list to get the correct name.
This works from a standard to standard library:
<?xml version="1.0" encoding="utf-8"?>
<soap:Envelope xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xmlns:soap="http://schemas.xmlsoap.org/soap/envelope/" xmlns:m="http://schemas.microsoft.com/sharepoint/soap/">