I use the tesa powerstrip that came with my headstage arrow amp to keep it attached to the J3. It works beautifully, and thankfully, the arrow is almost exactly the same dimensions as the J3.
The E7 has a screen though, so if you take that approach your unit would have a screen on the front (J3) and a screen on the back (E7). A little weird but could work.
In my experience I found that J3+amp sounds better than just a J3, primarily because I no longer use any eq/sound enhancements on the J3 itself. The more I used them, the more I learned to stay away from them. However, if you are ok with BBE and the EQ on the J3, you might not even need an amp, unless of course your portable phones are hard to drive.