I have an external Zero Charger that I use now and then on my FX 5.7. The FX has a lower rate charger than the S / DS / SR, and, have been able to successfully use both chargers on one socket at my home.
If using the J1772 adapter from Zero, I believe there are 3 separate C13 ends. You don't need to make a C13 splitter, they can be purchased fairly inexpensively. Just make sure that you get a heavy enough gauge.
I throw the Charger into an old backpack I used to use for a 17" laptop. Fits well enough with room for cable and a few extras. It isn't light, but, becomes noticeable after a while.