I feel silly. I loaded up the campaign after checking my mods were in the right order. I hadn't changed anything at all, but for some reason it worked perfectly. No markings of other ships at all. I don't get it. I played all night last night and there were green boxes with tails...
The only thing different was that last night I was just doing the torpedo training mission over and over, teaching myself how to use the various fiddly knobs. I was changing the realism settings via the Missions menu. When I just now loaded the (new) campaign, I set it from that wall map in the office. I exited the campaign and loaded the training mission, and the marks were gone there, too.
Very curious. Maybe you have to change the settings from within a career or it doesn't take. But, that wouldn't explain why the markings were disappearing up close when I checked it, but there when I unchecked...
Oh well, whatever. It's working properly now, no matter what the reason. Time to hunt!