Ok, this is a little bit gross, but it is possible to use the MIME::Base64::encode_base64() method to do the encoding, and you can specify that you don't want it to insert newlines. This works, but you have to be careful to decode the data on the other end (i.e. it doesn't happen automagically), because RPC::XML doesn't know that its payload is base64 encoded. It does know if you use the XML::RPC::base64->new() method, which wraps the data in <base64> tags). Not totally ideal, but I think I have my solution. :^)

Thanks to all for your suggestions!
-brian