It appears that demand for limited slip diffs (in the front) is driven by street racers who want a more balanced take off from a standing start. So if something fits the Element, it probably is a derivative of one developed for the Civic.
A search on the topic will turn up a number of threads. Some ask about ones for the rear diff (of an AWD), but the only leads that turn up are for the front. BUt that appears to be what you want, since your profile lists a 2WD.
Another option is to develop some finesse with the gas peddle. Even with AWD, I prefer to drive without spinning the drive wheels. Often that requires gentle pressure of the gas when starting. In some circumstances it helps to start with the AT in '2'. Honda's AT does not downshift when in '2', so you can start on slippery surface with less torque, and hence less chance of wheel spin.
Honda Ghandi put a quaife into the Hellement. They run about $1000. Its probably the best one you can get. I'm pretty sure that its a drop in replacement for the 2wd. The AWD requires some macining to work, but I think that STMOTORSPORTS was working on it.