I’ve embarked on a new tuning project, about which I’ll report shortly. But it occurs to me, as I’m pinging reeds after scraping, that for the approach you’ve been considering the pickup should be attached to the pinging device. I ping with a straight edge razor, as it’s light, easy to get the corner under the reed, and without risk produces very clear pinging. That wouldn’t provide a good mount for a pickup. I don’t really know much about pickups other than the standard kinds of guitar pickups, but I do believe that pickup via the pinging device would produce very clear readings, namely the kind I’m hearing in my pinging. The heavier and more inflexible the pinging device is, of course, the more risk.
I wouldn’t give up on your approach. The objective would be, I think, to get clean, consistent readings, and then make some determinations about the relationship between the “true” (pinging) tuning and satisfactory tuning for your playing. Possibly whatever issue there is here could be addressed by determining the pinging tuning relative to a slightly different standard.