nor shall be compelled in any criminal case to be a witness against himself
Generally, it’s held that you cannot be compelled to testify if there’s a reasonable likelihood that the response may tend to implicate someone. So you often can invoke 5A in civil contexts (which is why you’ll see people invoke it before Congress, or in civil trials).
One main difference is that in a criminal context we typically can’t draw an adverse inference against someone for invoking their fifth amendment rights. Whereas in a civil context we can. That doesn’t help us here much, though, because to my knowledge the NTSB is mostly interested in getting to the truth of the matter and not assigning liability or penalties.
One option to pierce 5A is to grant immunity for all testimony covered. So if the NTSB was pretty sure that the pilots aren’t going to be criminally charged for the incident (which they likely wouldn’t be), they could work with the DOJ to immunize the pilots for their testimony. That eliminates the risk of criminal prosecution for their responses, and nullifies the fifth amendment.
Hoping a note taker misses some salient detail in your favor is just trying to game the situation when you probably feel you're at fault. This isn't someone that committed a crime and is facing a judge/jury with possibility of going to jail. This is a licensed employee responsible for the safety of a not small number of other human beings. Some things stand to higher accountability
If the pilots won’t talk, they may be subpoenaed. Not sure if that means the 5th Amendment would apply.