Hello Mike and Members of the List!

If you are going to use two co-cathodes anyway, you might as
well switch between them. This can be done by a custom
modification of the AC full-wave rectifier circuit. The advantage
is that it should produce a new way of mixing, electrical agitation
of the charged particles in transit through the liquid. The power
source to the modified full-wave rectification can be whatever
AC voltage is desired from the wide variety of  wallwarts
available. The rectifier circuit can be breadboarded using a
general-purpose diode like the 1N4002. Four will be need
unless two LM334Z devices are used for a dual purpose as
rectifiers as well as current limiters.

The added insulation can be avoided by simply mounting the
coin so its perforated edge is above the water surface. Problems of variable 
contact resistance between coin and hook
have not occurred in my experience, but might be avoided by the
use of LM334Z's in the unlikely case it does occur.

Sophisticated timing can be done with the newer types of
Christmas light controllers. I just bought one at Lowes for about
seventeen dollars. It is a Timex  7 day timer that can hold
20 different switching schedules.

Whether your specifications can be met remains to be seen
through experiments. Mixing by electronic agitation may not be
strong enough by itself. Thermal mixing is axial and vertical.
Rotomechanical mixing is horizontal and tangential. Electrical
agitation is horizontal and parallelogram-zigzag, depending on
placement of electrodes. Maybe some combination of mixing
methods is for the best.

Best regards, and Happy Thanksgiving to all!

Matthew