A couple of things I realized after posting this......
- Even the convoluted method of creating a folder and populating it with seeds doesn't solve the problem. A folder named after the source VM still gets created at the root of the data store for the files besides the VMDKs. Something obvious that I missed.
- This functionality limitation is not only present in new VSR versions, but is inherent to vSphere 6.7 I believe. For example, when migrating a VM you can't choose a subfolder on the target data store. I think that could be done in earlier versions.