Gair,
I contacted the Eco One people and it seems that you can use dichlor with it.
Here's their response (directly from their email to me):
'Shocking with DiChlor is actually the preferred method for killing bacteria. However, you may want to use the non-chlorine shock occasionally in order to use up and oxidize any inactive chlorine in the system. Only shock with DiChlor AFTER using the tub or if you’re not going to use it for a day or two. Shocking with DiChlor will also get rid of cloudy water. Be careful not to shock to heavily and be sure to test the water before getting back in.'
I wrote to them after hearing that Eco One may help keep your skin moisturized. I may try it after the one month "Chas' Law" of changing the water on a new tub. I may also just use moisturizer if my family develops dry skin.
Hope this helps!
Vinny