Why do you need one so small? I think you may have a real problem finding such a thing, because the electrical box in the ceiling, where connections are made between the light fixture's wiring and the house's wiring, is likely to be bigger than 4" across, and the canopy has to be big enough to cover it with room to spare. I don't have an encyclopedic knowledge of available components, but my intuition tells me you're looking for a part not likely to exist.

Please do NOT SPAM us! OK, forget the please. NO SPAM!

For the uplight, you could go a few routes, especially with respect to dimming functionality. And some fixtures don't support dimming, so you need to figure that out. To that end, I suggest you think through the use cases. For example, the use case that I think I'd appreciate most is late evening, after you've retired to another room of the house, at which time a mellow indirect glow from the skylight cutout would be particularly pleasant. You might also want the more light from this source on occasion, in which case you'd want brighter lights on a dimmer. That being said, here's some options. I'm thinking two, centered on the skylights, mounted near the bottom rim of the cutout (just above the beam probably). Regarding the pendant, I know that selecting pendants is hard enough without more to think about, but one downside of a single pendant vs multiple pendants is thhat single sources create worse shadows. And the clear glass pendants above exacerbate this harsh shadow problem by being point sources, whereas the Fillsta, for example, mitigates this problem because it's effectively a uniform 31" sphere of light. This large diffuser also makes it possible to use a brighter source. For example, you could put a 300W equivalent CFL in the Fillsta, but such a bright light would be unacceptably harsh in a point source like the clear glass pendants above.

So far everyone has been in agreement. I'm also not a fan of track lighting, but that is what came with the house and it at least works. Can lights over the sitting area would do the job, but that would be pricy and challenging DIY, for another solution that isn't really attractive and we don't often use for more than a 15-30 minutes per day. It is a tricky problem, as we have a lot of furniture already packed in there, and I don't really want to obstruct the sight lines to the garden (we have a 10' wide slider where this house's French doors are located). Maybe I will experiment with finding a much brighter floor light for behind the seating, and hiding the torchiere floor lamp behind the entertainment center, for when we just need a little room illumination.