ozzy,
It is interesting that only beginnings of WAV songs are not displaying covers. Could it be that it simply takes a little time for the machine you are playing it on to digest and figure everything out? It does happen on one of my players, but I am talking about a second or two and even that not every time. Check if it is every time with the same song.
I abandoned automated retrieval of cover art from the Internet. Too many errors (wrong pictures). In fact, it is worth checking even song titles, etc. They are also less than perfect.
Now, when you started your project of tagging, you will be in it longer than you think, I am afraid.
Once all the covers are done, you may notice that The Beatles and the beatles are filed separately and may end up in different folders. That is just a made-up example, but I want to say that arranging the library becomes a year-long chore and you may be tempted to straighten it out. It took me longer. If you have lots of classical, I feel for you.
I second mapman’s thoughts about WAV and FLAC. I converted (actually copied) from AIFF to FLAC. I used AIFF initially because it does take cover art more or less well. Virtually any car these days will play FLAC from SD card or USB drive and it displays covers. Not so much with WAV and not so much with AIFF.
Be careful not to do all of this "cover work" and then convert to FLAC. There is no real guarantee all of them will transfer although dBpoweramp does a decent, if not consistent, job with that.
I would copy all I have to FLAC and only then start adding covers, arranging names and nunbers, etc. Been there, done that, would do it this way this time.