After tinkering with deinterlacing settings, I've determined I get the most overall watchable results from bob deinterlacing the entire thing to 60p.
This isn't a perfect solution. For example, the goal is to use this with DS9/VOY, but I'm pretty sure all the CG effects on both shows were done at 30p, so I'm doubling frames for those scenes, and then I'm technically butchering all the film-shot elements. 24 does not go into 60. It divides to 2.5. What this means is, running at 60p, some frames will take up 2 frames, while others will take up 1. This should cause jitter in the output, but if I'm correct, all I'm really doing is accurately replicating the jitter present in the source - that is to say, it wasn't too horribly noticeable then, and it shouldn't be any worse here.
I wouldn't have to do any of this if Handbrake's interlace detection worked worth a damn.