Yes, I have come across this plant and berry infrequently in the mid-elevations of OR and WA. The berry tastes very similar to a standard garden-variety black-cap black raspberry.

Once incorporated into a slurpee or popsicle, I cannot image a person could tell the difference from R. occidentalis, the commercial blackcap.

OK, I think I see what you're saying here. As an easterner I've probably never had a "commercial black-cap black raspberry", but you mean that commercial fruit also is similar to the artificial "blue raspberry"? Well, great...now curious to try one in the garden. The Himalayan bramble is quite happy to be a weed here so it's hard to imagine a PNW cultivar should have too much trouble with our hot summers.

Oh...wait...now I see the commercial one is actually native to the east but more commonly grown for commerce in Oregon. Figures. I'll have to seek out a pick-your-own somewhere near me to find these elusive black raspberries.

FWIW I probably missed the chance to find these at a farm, but I was up in Lancaster Co. and saw a jar of black raspberry jam at a farmer's market. I figured I'd try it. Indeed one can discern the similarity to the artificial flavor known as blue raspberry. There's definitely a quality not shared with raspberries or blackberries. So that part of the mystery is solved at least. I wonder why I never encountered this flavor before.

Do the various hybrid berries like the Marionberries just taste like combinations of the 3 main types (raspberries, black berries, and black raspberries) or do any have a distinctive, 4th note?

Well the hybrids taste like something in-between, not really unique, just somewhere between a blackberry and raspberry.
From what I got out of what Larry said, is R. leucodermis tastes like any other black raspberry, which does have a different taste from red or yellow. Yellow raspberries also to me taste different. Especially in jam. The red anthocyanins bring a bitter taste to the mix. Thus yellows are sweeter. Although any yellows bought tasted terrible! I would never buy them, the ones from the garden are ton's better.

R. leucodermis is supposed to be not as great tasting as R. occidentalis - the linked study compares growth and fruit characteristics of a few native R. leucodermis populations to commercial black raspberry.

Here is a link that might be useful: R. Leucodermis study

Cool, I have those in my back yard growing wild. I just thought they were strange black raspberries that tasted better while still purple than if allowed to stay on the bramble longer.

They seem to taste a little better than the wild black raspberries here which are more insipid, but not as good as Jewel or other cultivated black raspberries.

Our wilds here are small, but the flavor is excellent for jams. It has beat all my domestics in taste tests, hands down, leagues ahead. I would try jam with the wilds.