Haven't been noticing any of this.
You can get your channel back if you oppose the copyright strike and win. That would of course require that you actually own the rights to upload the song, otherwise they're in their full right to strike you.
Covers are considered works of their own just like any other original song, almost, so they are reinforced by copyright in much the same way. They aren't necessarily safer unless the copyright holder of the cover is more accepting towards Nightcore.
Some techniques used to protect yourself are:
1. Hide the full song title by never including the artist in the video title/description, instead adding it through cards/annotations/or in-video text. This makes it much harder for copyright holders to find the video in the first place.
2. Don't monetize. A monetized video is uploaded for profit, a non-monetized video is uploaded out of passion. From my experience people seem to find the latter more acceptable.
I personally like to say something nice about the song in the very beginning of the description, so it's the first thing anyone sees. Don't know how much that actually helps, but it might.