A couple of thoughts, based on my experience doing pretty much the same thing with a barleywine + porter partigyle:
You might not get as much color as you think out of your second wort, so if I were you I'd double the Black Prinz to 8 oz.
I don't think there's any need to mash the oats and black for a full hour. 15 minutes in the 150s should be sufficient to convert the starches, or if you're concerned, go 20 minutes. And this will help also for my following recommendation...
If you want to guarantee good attenuation from your barleywine, and not such dry attenuation in your stout (with a final gravity of like 1.006 or something crazy like that!), then you could plan to boil your stout first, and let the barleywine wort sit for that couple hour period to dry out a little more. Worked for mine.
Or I guess you could do a mashout on the barleywine while those oats are sitting in there, if you want to lock in sweetness into your barleywine. But regardless my point is really that you want to dry out your barleywine, rather than leaving your stout to sit at mash temperatures for an extra hour to dry out this small beer even more than it already will be. For my second-runnings porter, it was so dry that I also had to add lactose to sweeten it, even though I boiled it before the barleywine. Something to think about.