Thanks to another message from Chris Chapman, I've now arranged the gold rods in this way:
Assemble one pair on the metal backing (I'm using a shelf
Assemble a second pair and slide it up next to the first such that it would repell, except for the friction between the magnets and the bracket.
Note that the north-south axis of the magnets is alligned about 45 degrees from the vertical. An end view would look something like this:
The next pair of magnets up the line would look like this:
With this arrangement, as Chris points out, the magnetic field at the N-N and S-S junctions will be reduced, but not nearly as reduced as when the junctions are N-S. With this arrangement, the period of the graphite rods was increased. The arrangement below uses four pairs of gold rods (with some extras rods on each end) and two 0.7 x 60 mm leads glued together with a small overlap. The period is between 1 and 2 seconds. The lead seems to have properties that are not uniform, as it would could not be balanced in a totally symmetric position and reversing the lead end for end caused the same end to overlap more. The white pieces are plastic rods used to keep the graphite from running away (thanks to a suggestion by Chris!)
Click on the photo for a view of my "work" area.