I'm not sure what platform you're using (I'm on Linux) but for what you're trying to do, I get the best results with Mixxx. This is meant as DJ software, but it is useful for field recordings because you can see your whole waveform, and you can even add cues and label the cues. And, it's cross-platform.
The cues are useful when you need to tag a point in the recording that isn't obvious from the waveform. For instance, if you're recording a rainstorm, and there's a single thunderclap, you can see that pretty clearly in the waveform. But if you're recording a brook and there's distant birdsong, you might not want to sit through 20 minutes of recording, trying to find that part.
Mixxx allows you to create 'crates' and playlists. Crates hold tracks in no particular order, with no duplicates, where playlists are in a specific order and you can have the same track more than once. With crates, you can organize your recordings: 'Talking', 'Weather', et cetera.
I don't keep WAV files anymore, and I know these don't have the same tagging scheme as MP3s; FLAC files do, however, and they are smaller than WAV files, without losing sound quality. So if you use FLAC, then you can just set the actual date of the recording in the 'date' field, and yes, you can do this in a batch in Mixxx, and have it write to the files.
However, you might also not want tag edits to write to files. For instance, if you have a backup or sync system in place, and you bulk edit metadata for your recordings, then change your mind and change them again, well that's a lot of binary data to synchronize. You mentioned photo/video software, and they usually resolve this issue by using a sidecar file that holds the metadata. In this case, you could just sync your Mixxx db file when it's updated, which is way smaller.
If you ever decide to move out of Mixxx, you can go back in and have it 'bake' the tag data into the files themselves.
Another Mixxx feature is called 'Auto DJ', where it'll pull a bunch of files from a selected crate and crossfade them in a random sequence. I have created a crate of recordings that I can sleep to, set my in / out cues to exclude anything on the recording that might wake me up (like talking or thunder), and just have that going all night. You can even just loop a field recording and leave that going forever.
The one thing Mixxx won't do is normalization, but it does have replay gain, which means it'll 'normalize' your recordings without altering the recording itself. For permanent normalization, you'll need a program like Audacity.
Anyway, I have been in the same boat as you. Apparently, there is no software for field recordings (though one would assume there would be), but you can use Mixxx "off-label" and it does a great job.