Entry 1 is very close to what I had envisioned. Can you make the bottom of the letters a bit more visible so they are more easily identified as LMI? The L right now looks too much like an I. The audience is very literal.
Entry 2 is very classic and gives us a good mark to use in a variety of situations.
Same with Entry 3. The circle with the LMI could be used an its own.
I personally enjoy Entry 4, but think with all the letters overlapping, our intended audience may be confused.