Update: On January 12th, I emailed Kobalt Music Publishing to see if there had been any development regarding clearance from the client of their track I used in my mix. A couple of days later, on January 14th, I was told that there hadn't been any feedback and there likely wouldn't be, as these things take time. I was thanked for my patience. On January 24th, 10 days later, I'm still waiting...

Note: What sucks about all of this is that even if I'm given approval by the client, my mix will have lost a lot of views. Here's how. When you post a mix to SoundCloud, it shows up on the feed of everyone who is following you, kind of like how your friends who are following you on Facebook see a status you post. But since my mix was immediately taken down, all of those people who would've seen my mix in their feed won't, unless they visit my page themselves or find my mix in some other way.
To continue the Facebook analogy, let's say that just before you post a Facebook status, you set it to "Only Me", which hides it from everyone (aside from yourself, of course). A month later, you make the status public. Well, by that time, it would have lost its "organic reach": few will see it because it will now be lost among everything else you've been posting. From the standpoint of someone who is trying to gain exposure, this is really infuriating.
This might be a dumb idea, but SoundCloud should create a catalogue that allows users to search tracks that are flagged for copyright infringement. Remember: some record labels allow their tunes to be used publicly, like in the form of a mix, without their explicit consent. So, a DJ or producer could search a track in the catalogue and if they see that if they were to include it in a mix, the mix would be taken down, they could, in advance, choose to seek the necessary authorization or just not include the track. This would save everyone a lot of time and frustration.

Hope you're all having a nice weekend.