The reference track probably qualifies as fair use, so long as copies of the track are not digitally distributed by @holster during the course of the competition. That's not a problem. Re-creating a track is. Actual damages are lose the compulsory licensing fees they are entitled to under federal law, and violate the rights to derivative works and duplication.
The artist probably doesn't give a shit, but the publisher probably does. The artist just might see it as free promotion, but the publisher doesn't stand to benefit from the free promotion in the way an artist might.
If someone threatens to sue, they're threatening to come after more than $750. Actual/compensatory damages (which means what the artist actually lost) of $750 are the minimum required to open the door to add hundreds of thousands to the claim in punitive (which means don't do this again) and statutory (which means you broke the law). So if you hurt the person for at least $750, you get spanked 10x over so you don't do it again, and another 10x over because you know you shouldn't have done it in the first place. By the way, you're also liable for court costs in a copyright infringement claim.
No one here is going to get sued. Yes, I know that. First someone will get asked politely to not use particular material anymore. But if you stubbornly refused on the grounds you just named, you'd be surprised at how temperamental publishers can be.
Why are you so insistent on using a song without permission? Just ask for god sake. As I said earlier...just 'clear the song ahead of time'.
Because when @Chordwainer covers a track, he's not intending to make it the centerpiece of an online competition.
I do have my facts right. Singing a song at a voice lesson is fair use. Performing a jazz pieces at a senior recital is fair use. A recreation for a bash is fair use. Featuring a song as a competition material for performers to compete for scholarships...yes. Featuring it as competition for us to re-record, no. Students video taping themselves as part of their audition and privately submitting it to a university ok. Us re-recoding something then publicly posting it on the open web? Wouldn't try it without permission.