Alrighty, here's a crash course on what should be done to correct the looping issues. Since I can't actually give you the file, this is something you all might want to try if it is really bugging you. To fix the issues, this only took around 30 minutes to complete, and around an hour to get everything online. Sorry for the delay on the post, but work got in the way....
Anywhooo....
First open up your sound file in any sound editor program that allows you to have control with crossfades, volumes, pitch, and other stuff that might be useful. For this example, I used Sony Vegas since a lot of filmers use this for their videos. Preferably, Sony Soundforge is a much better program for this, but Vegas does the basics as long as your input sound is clear and crisp.
Next, find where the file is starting to level off before the engine really starts to spool up. Cut a 4-5 second loop from your source file.
Move the final piece all the way over to the side so you cannot change any of the settings while you play around with some other things.
After that is complete, select your 4-5 second loop and copy/paste it a few times.
This step is very important. Since the soundset has a continuously increasing pitch sound, we would need to inverse some parts so it doesn't sound like a broken record but rather like butter on ice.

Since my loop was only for a few sections, I only needed to do this twice to make it sound alright.
I zoomed out to show you guys the "Proper looping wave

". I also moved the piece from the tail end of the clip and slid it right beside the loop file with no crossover. The other "looping parts" have a .162 second crossover. See how it goes down, then back up to meet the next clip? Having a crossfade helps to minimize anything that might not line up exactly. Though, you should try to stay away from this if you can work on it even further.
Right click on the sound file to see what format, quality, and bitrate the original clip used. Mark this down on a piece of paper somewhere and keep it handy and legible.
Select the entire clip from start to finish, and make sure your program has everything you want to hear highlighted/selected in some fashion.
Go up to your rendering options and punch in the information you wrote down on the sheet of paper moments ago. Save this new rendition as the exact name of the file.
Now, go into your sound folder, back up your original file by appending a label with something like... A320enginestart-01.wav_BACKUP.
Paste your new file into the directory which your sound files lie, and voila! You're set!
Now, for the audio test...
[youtube]Io0GzVw3ImA[/youtube]
Sounds pretty good right?

Also, you mentioned that the file needed to be 37 seconds long. You could also do the same thing with cutting, pasting, and flipping as I did with any other sections to get the extra two seconds you need. Hope this helps!