soapysteven,
I am going to approach this from the angle of the copyright owners and hopefully give you a better understanding of your specific situation.
To start, fair use is not a compulsory claim, in that anyone can use copyrighted material, claim fair use because it falls under a certain criteria, and then they are automatically granted the right to use the material by law. Fair us is a defense against being accused of copyright infringement. When infringement is suspected, a copyright holder looks at the use, then makes a choice on whether they wish to take action. The accused infringer can state their case to the copyright holder, but that doesn't mean the holder cannot disagree and attempt to take further action.
You have 3 main copyright holders involved with your videos: Record labels, songwriters/publishers, and music video producers (probably labels as well). Billboard Magazine may also have a claim. If you claim you are using their material for review, criticism, and remix they have a strong case to state otherwise. Here's why:
First, there is no review or criticism taking place that cannot exist without using the material. All that is being shown is a countdown. Technically, that can take place without the label's copyrighted sound recording, the songwriters copyrighted composition, and the copyrighted video. Their argument would state that you can relay the exact information without the music videos by just scrolling a list across the screen. It may not be nearly as entertaining or engaging but "it would be boring without the copyrighted material" isn't a valid defense. Unless there is in-depth commentary of the song, artist, and specific clip of video, the defense is not there. And again, it's only a strong defense, not a compulsory guarantee.
Second, the remix defense isn't valid because the clips are exactly in their original form and completely identifiable. Just ask The Verve about this one
Last thing to note, is given the format that everything is presented, Billboard may have a claim. It is true that copyright does not apply when stating fact, and without this no one could ever communicate the news. For instance, to say "The Verve" was sued by "Rolling Stones" members Mick Jagger and Keith Richards over "Bittersweet Symphony," is a fact, and there is no valid infringement claim for the use of band names and song title. You are stating facts, but with Billboard most likely being a trademarked name, and that name existing in your Titles and Tags, the argument could be made that you are attempting to veer business away from a product (music charts) they provide, to yours (also music charts) with use of their name, or even attempting to appear to be endorsed by them. It maybe a different story if you were to site them as a source only, in your description for the information you are presenting.
So, what does this all mean when it comes to monetizing? It all depends on how the copyright holders wish to proceed.