I submitted a conference paper that was too long...what now? I'm a MA student, and I think I've made a big mistake submitting to my first conference...

I submitted an abstract to a regional academic conference over the summer, and it was accepted. I had to submit the full version of the paper for the student competition a few weeks ago. I was having trouble cutting my material down to meet the limit-- all the conference said was that papers should be "no longer than 20 minutes." The due date crept up on me, and I did my best to cut it down as much as possible, not having enough time to read through my drafts out loud to see how "long" they were.

The conference is two weeks away, and I have started practicing out loud...and it's taking me around 27 minutes to read my paper. What do I do? Is it a big faux-pas to shorten my submitted paper for the presentation so it doesn't go over the time limit? I've had trouble getting in touch with the conference organizers about other things, so I'm doubtful that I'll be able to talk to them about this.
Keeping in time is mandatory

In general, you can expect to be cut off if you are over the time limit, so you definitely should shorten your presentation - it's very likely that important parts of your talk are at the end so it's very important not to lose the ending!

In most fields, presentations are very, very different from the actual content of the paper - if someone wants to read the paper, they can do so at any time; but the presentation should cover why they'd want to read your paper afterwards and also explain things that might be easier to show or demonstrate rather than read about.

Even if in your field tradition is to read the paper as-is, that is optional but keeping the schedule is mandatory. I would suggest to reduce some parts that describe the background/foundation/earlier results which would be known by the conference attendees but might be less known for a general reader of your paper. You should mention earlier work, but you don't need to go into detail about that even if you do so in your paper. 

Keep the focus of your talk on the novel parts of your paper, and also make sure cover in detail the motivation of this research and it's wider context in your field.