i have both the LX2 and E2DL, and just tried exchanging its heads after reading your post.
the LX2 head on the E2DL body is a single mode light with high only.
interesting enough, the E2DL head on the LX2 body and tailcap behaves exactly like a regular LX2, you get the momentary low and high.
If you want just the E2DL head, check the CPFMP from time to time... One was sold few days ago for $60...
I think you might be looking for a single level KX2C head that has been cracked open and swapped for a ED2L bezel (if they are compatible.)