Interesting. From the outside, at least, it looks like your coronals are simply unspecified for voice and then acquire it from environment.
That's certainly a novel and interesting idea that I haven't thought about.
I always enjoy looking at your datasets, but I tend to be at a loss for good answers since I don't know much about Germanic. I'm glad lx is back around, as he's probably got some insights.
It's good to have him back!

Generally speaking, though, it's not a problem for an alternation to acquire contrast in one dialect but remain free in another. In fact, along with direct loan vocabularies, that's the major mechanism of phonogenesis.
Actually, the voiceless initials stem from Old Norse /hC~C̥/ from Proto-Germanic */hC he/.
*hnakkô m. → hnakki m. → hnakka m. "neck, nape"
*hliþą n. → hlið n. → hlið n. "door, gate"
*hrabnaz m. → hrafn m. → hrafn m. "raven, corvine bird"
*hernô m. → hjarni m. → hjernu f. (*hjerna m.) "brain" (reanalysed as feminine; cf. Sv.
hjärna with feminine -a suffix, OSv.
hiærne with masculine -e suffix)
*hwalaz m. → hvalr m. → hval m. "whale"
Since I don't have the means to collect the required data, I cannot say how many (proportionally) use the voiceless initials. However, based on my intuition and experience alone, I would say it's going to be fairly high.
The dialects where the [kC̥~çC̥] variants are used the initials are undoubtedly phonemic — contrasting with [C]; dialects where initial voicing contrast has been (partially?) lost there wouldn't seem to be any perceived contrast (non-phonemic) but do still to some degree (varies from area to area and person to person) of variation where the phonemically voiced initial can still be realised with either ambiguous voicing or as outright voiceless, but importantly,
without contrast.
So it's probably a bit of both. The voiceless initials are still partially there (cross-dialectally), and influence from nearby dialects still allows free variation where voicing has been lost, which in turn might lead to (or has lead to) them (perhaps) reacquiring (partial) contrast.
In fact, along with direct loan vocabularies, that's the major mechanism of phonogenesis.
So reacquiring a (perhaps partial) contrast due to influences from nearby closely related dialects is not such a crazy idea after all?
Words do sometimes seem to flow fairly unhindered between the dialects, so even though there is strictly no contrast in the local dialect, continued exposure from the nearby dialects still maintains some "wont" or "accustomisation" to the contrast.
Even though I call them dialects, they
are very close to each other.