Not a perfect solution, but you might look for a third-party program that automatically mirrors files from one location to another.
My NAS has software that does this, so I ingest the files to the local hard drive, then it copies them to the NAS in the background.
Because it's a background process, I don't have to wait for the copy to finish before I move into culling and editing.
You're trading the security of knowing you had two backups to get started sooner, but I'm always on the computer long enough for the sync to complete before I wrap up, so it's worth it.