Our apologies for the delayed followup. The transfer service does support this today -- it may not appear to be possible in the Console GUI, because the GCS bucket browser widget doesn't show buckets in other projects/organizations, but you can actually type in the bucket URL manually (ex: gs://my-bucket-name), and the transfer should work successfully.
Note: as with all GCS sources/destinations in the transfer service, you will need to make sure the transfer service account has access to the destination/source buckets (
instructions), similar to what Elliott mentioned.
Best,
Ash (Product Manager for the Transfer Service)