Ooh. Tough one.
I think it's interesting you mentioned specifically AAA or Cr123 lights but not AA. I think you're going to find most High CRI options in the AA format just because they are more popular. The ones that stand out are the Zebralight H53c/Fc, H502c, and H502d. The first is a typical reflectored angle light with the Cree XP-L2 Easywhite. The latter 2 use Philips Luxeon emitters with the c being 4000K and the d being 5000k. All are high CRI but none are Nichias.
Zebralight doesn't offer their H3X series lights in all these emitter combinations unfortunately. Only cool and neutral. That said, I have both H3X (Cr123) and H5X (AA) series lights and they are hardly different in size. The AA variant is slightly longer while the cr123 variant is slightly girthier in the tube. Both share the same size head and both are among the smallest sized lights in their respective categories.
There are a couple AAA angle lights coming onto the scene including the Maratac "TPF" light and the new Manker E02.
The Maratac light is quite small but has a twisty UI which you may not like. It's also pure flood.
The Manker is a little beefier and in fact, it's scarcely smaller than the AA Zebralight (72 mm long vs 75, and 20mm in diameter vs 21.8). It's also no lighter than the Zebralight when you compare their weight with no batteries (Zebralight is actually lighter at 31g vs 32g). That's not much of a size savings for losing several times the battery capacity.
In short, I'm not aware of a current gen, high CRI CR123 or AAA angle light. Of the CRI options, I'm aware of only the Zebralight AA options, and none use Nichia LEDs. However, if you aren't limited to just the Nichia, there are several standard/flood models with a variety of high CRI tints and efficiencies available. In reality and especially in practice, they are not larger than a corresponding AAA or Cr123 model, and they offer they broadest choice of power sources (alkaline, lithium primary, lithium ion, and NiMH).
Hope this helps.