There's definitely a few morals to this story (but note: not legal advice! I am not a lawyer!):
1. You should keep your own copy of anything you sign as part of your employment contract.
2. You should maybe keep a record of when you handed that to your employer ("I did in fact sign a copy of the NDA when I began my employment, and handed it to [person] on [date]. I hope this helps you to locate it.")
3. If the NDAs are so long that it would be impractical to visually diff them, you can just ask the company: "Can you please ask [name of company lawyer] to send me an email confirming that this is the same NDA that I signed at the beginning of my employment on [date]?" If they do, and then later rely on a clause that has been inserted, I suspect they would have a hard time convincing a court to enforce that clause.
4. In the author's situation, they sound like they were over a bit of a barrel economically and it's hard to push back in that situation. If you are willing to push back, remember that your employer is asking for something from you, i.e. a change to your contract. And if that change is that they can audit your personal devices, that is not a small concession! "This NDA does differ substantially from the one I originally signed, and would represent a significant change in the conditions of my employment. I understand if the company has new security concerns, and I am willing to work constructively to find an acceptable solution. For instance, if you are uncomfortable with me being able to access work e-mail on my personal device, you can issue me with a separate device over which you would have auditing rights."