On the iPod’s Movies setting (“my device”) there are no duplications showing.
That probably means selecting the movie (on that screen) makes the iPod try to sync BOTH versions. It may show them separately, if you change the name of one of the two versions. For example, you can add "(iPod)" to the end of the names of videos that were created for syncing to the iPod.
But, I can't tell which one was created for syncing to the iPod, as I mentioned below.
I can’t drag and drop the “converted” version as far as I can tell into a new playlist because the listing doesn’t seem to distinguish the new version from the old.
On the list showing your Movies library, show it as a simple list, if it is not already. You can do so by clicking at the right end of the horizontal bar, where there is a "toggle" for how the list is shown; select Movie List.
It is already showing as "Movie List."
Is there currently a list column for Date Added?
I've now added such a listing
You may want to do that again, and select Kind.
OK, did that
With Date Added visible on the Movies list, it should be easy to distinguish the new version. Also, you can note what the Kind is for those new videos.
OK - all but two are showing as MPEG-4 videos; two are QuickTime movie files.
Also, on my iPod’s movies settings screen I don’t see “include movies…” at the bottom. I see an “add to” at the top of the screen...
I don't see Add to at the top of that screen, so just to confirm we are on the same screen (iPod's Movies settings screen), select the iPod in iTunes so that you initially see the iPod's Summary settings screen. In the sidebar, under Settings, click Movies. To the right is the iPod's Movies settings screen. You may need to "scroll" the screen to see the Include Movies from Playlists portion at the bottom.
Yes, I'm on that screen, and now I see the "include Movies from Playlists" option.
OK, I've gotten this far but mind isn't clear on the next steps to take. Would you mind repeating the steps again?