But can you imagine how expensive it would be to do that for 4TB of data?
It would depends on how much a 4TB HDD cost in your place. Also, you need to ask yourself what do you really need to backup among that 4TB.
This is also not a fix for my current problem.
Maybe, but it can help recovering your data.
It's only ever happened following a crash, which there is no "explanation" for.
Crash in the program or in the OS?