My job search took much longer than I'd expected. It helped a lot that I'd been using Beeminder, because I could see that I had indeed been putting in a reasonable amount of effort. In the past, when I've had trouble finding a job, it was always due to the fact that I hadn't really been working effectively on the search process. But this time I had evidence that I'd been doing my due diligence - it just wasn't working.
After about 3 months of searching and basically no responses, I finally was forced to admit that the sorts of jobs I was looking for weren't available to someone with my qualifications - and if they were, the pay wouldn't cover my cost of living. So I decided to look in other areas. Almost immediately after broadening my search, I got an interview for a position that is pretty much my dream job. And I got the job! I've been working there for two weeks now.
It was a tough decision to make the move across the country, but the combination of Beeminder and my application records gave me proof that (a) I wanted the job, as evidenced by my willingness to keep paying for Beeminder to keep me on track; (b) I'd been making as much of an effort as I was realistically capable of doing; and (c) despite that, the search just wasn't working - and I couldn't afford to wait indefinitely. Having that proof made the move feel like a strategic decision, not just 'giving up'.
The concern I mentioned in my original post turned out to be a non-issue; a couple day's worth of in-person interviews gave me enough of a spike at the end that I could have just archived the goal. But I emailed support so that I could have it accurately reflect the end date, which nicely concluded what may be the most interesting graph I've created so far:
Thanks for all your support!