That does not sound like your LS is behaving correctly. Could you post some pictures of the front and back of the board as well as all the outboard connections (jacks, pots, etc.)? Please make them close up and sharp or they may not help to spot an error...
*EDIT* There is another misunderstanding in your email: the pots are SENSITIVITY and ATTACK. The SENS knob is used to tune how the pedal reacts to your signal and will be different for each guitar/pickup type. The ATTACK knob controls how long the swell up will be. The SENS knob also has an effect on how much sustain you will get (which may have caused the confusion). I would try the SENS knob at 9 o'clock and work from there to readjust the trim pot (with ATTACK fully clockwise). BTW, I much prefer the 5457 over the JFET.
It's usually a little fiddly to get the SENS knob correct for your setup, but once it's set it should work nicely: http://www.pantanosoftware.com/Music/SprocketDemo1.mp3
The first part is with a cap that slows the swell, the second is with the stock cap. I prefer stock, as the pedal is more responsive to my style that way.