That's where I see a Catch-22. You need a specialization to get hired, but in doing so severely limit your job options. Of course, in some sense that is a side effect of demanding specialization in the first place.

I did real-time radar signal processing for six years, and hardware production support on radar electronics for 3.5 years prior to that. I can't convince anyone that these experiences are easily transferrable to other areas such as robotics and medical devices. In fact, I don't even get the chance; hardly anyone will even give me a phone screen. Yet I have been doing NLP for the past three years and can't get recruiters to leave me alone about it.

Well, you want a reputation as a "go-to" person. The ability to get your fingers into all kinds of pies can be pretty interesting (as in: when layoffs have happened, you are more likely to survive because you can work on anything).

Some organizations don't like this. They want to pigeon-hole you as "the mouse driver guy" or whatever, and when your company stops making mice you're in trouble. Avoid these places if you can.