Reincarnation of a Lovebird

How about this recording? It's not a race.

 

OK, I guess they'll know you're not rushing but another selection with the desired tempo might be something to consider.

 

No shortcuts, start where you're comfortable and keep pushing the tempo up. When poopie falls apart at a tempo, start pulling it apart to see what's causing the obstacle. If you're fingering a problematic phrase in one position, try shifting between different positions. If it's shifts that are causing the impediment, try fingering across one position.
Another suggestion, stop reading the head. Listen to just the melody many many many many many many many many many many many many many many many many times a day. So if somebody drags you out of a deep sleep at 4AM you can sing all the pitches and nuances of phrasing accurately. THEN play what you're hearing.

 

Also, while ambition is considered a wonderful thing and playing it safe is certainly not anything to be recommended, playing something you've worked up and are unable to execute without a lot of effort isn't really going to be met with as much positive feeling as you really making a meaningful and personally revealing musical statement with material you're more familiar with.
To say it another way, they're not really going to care how hard the tune you shaged up was. They want to hear how you SOUND.

 

A little hard to assess without actually hearing you play, but for most of us, you have to hit stuff A LOT in the shed before it starts leaking a little bit into day to day playing. You want to get this stuff deep into your ear, so play it every time you have a session, every time you play a gig, play it in different keys, play it in 3, play it in 5, as a ballad, as a bossa, make up lyrics to the melody.
If you haven't checked it out, look at a stickied post called REALLY Learning a Tune in the Music Theory forum of the DB side. Use the section where you play only 3 bars of melody in every 8 bar section and improvise the other 5 bars. The melody has to be in three different bars in every 8 bar section. That is, if you start the melody on the first measure, you can't start any other melody phrase in the first bar of a section, etc.

I'm not sure what you mean when you say "hit the ceiling", when you also say you haven't been able to execute the melody at the tempo you're trying to hit.

 

There are a few other things to bear in mind:
1. unless you're looking for scholarship money, the New School is pretty easy to get into. Auditions are more about assessment for placement
2. bassists, and particularly double bassists are almost always at a premium. You'll have the opportunity to play "above your pay grade" a pretty good bit
3. when they're assessing you for placement, they're also trying to determine where your strengths and weaknesses are, which is good for you. You want to turn your weaknesses into strengths and you can't do that if you've managed to "hide" them by, for instance, working up something to play over GIANT STEPS while in reality you have a hard time improvising in the moment on something like AUTUMN LEAVES. Yes, you can't study with whoever you want to if your audition says you need some remedial work. But without the remedial work, you won't be able to fully benefit from private lessons.
And on that subject, be very, very careful about who you want to study privately with. I know a lot of folks who come to the New School with the great idea of being able to take private lessons from REALLY GREAT AND FAMOUS BASSIST WHOSE 100s OF RECORDS I HAVE only to find out that they have to cram a semester's worth of lessons into 3 weeks because RGAFBWHORIH has been out on tour the whole time. Or, as happened to a good friend of mine, have his first lesson with Pharoah Sanders consist of listening to Pharoah try out reeds for 2 and 1/2 hours trying to find one for his gig that night.
I'm just sayin'...

 

And not to totally belabor and flog, but maybe e-mail Mike Karn, who posts at this site and who is on faculty there.