Ok, I redownloaded the album from HD Tracks. They still do it.
However, I've now found that I am able to get the tracks to play correctly in Original mode (without transcoding enabled). I'm fairly certain I tested that this afternoon though (but the clients I was using I do typically keep in converting mode). So maybe a broken MP3 or something is stuck in a cache somewhere? But if so, I can't find them anywhere. I had, until a moment ago, conversion cache turned off on my server. I turned it on and pointed it at a new empty directory to make sure that setting wasn't mucked up somehow (and the folder it is pointing to is still empty). I also went in and, with MC closed out, cleared out cache folders in AppData and my Library folder for good measure. Nothing helped.
So, maybe I failed when I tested in "original" mode somehow? But I clearly remember switching both MC and JRemote to Original mode earlier and testing (as I was writing my original post, in fact).
I also tried re-importing them completely from scratch in case it was some crazy behavior of the particular file tracks in my Library. No change in behavior. So now, with Conversion disabled, they work right on both JRemote and MC clients, but if I enable Conversion, they still cut off half-way through.
I'm stumped.