David cgc, thanks for the insights into what's going on in LightWave. The good news is, I think I found a partial solution to my problem, at least for the scenes where the stars are not streaking past the ship at superluminal velocity (i.e., the Constellation and Enterprise aren't flying at warp speed).
One of the things that was really bugging me (besides having to use LightWave's render engine) was the twinkly results I was getting with stationary or very slow-moving stars, even with a ton of anti-aliasing and doubling the resolution as described above. Then I remembered that OctaneRender has a "visible environment" that you can apply as a backdrop, just like in LightWave. So, I shot a flat plate of my starfield with the camera not moving at warp 7, and rendered that at 16384 x 16384 resolution. After some post-processing in Photoshop to turn the planar image into a spherical one, I used that as a spherically-mapped background in OctaneRender and voila! Success. I can point the camera in any direction and it looks like I'm surrounded by a field of stars infinitely far away. 4K images render in 5 seconds or less per frame, which is more than acceptable.
I've still gotta believe there must be an "Octane way" to render my stars-at-warp, but since the "Doomsday Machine" project won't need too many of those I'll defer further investigation for the next project. Probably something with volumetrics/VDB. We'll see.