Gary wins the prize!
Problem still exists
It turns out that this EVSE, and possibly all the EVI MCS 100-3, was specifically programmed to only allow a single cycle. I learned this by speaking with Matt, Gary and Jason at Clipper Creek. I believe it was Jason who was one of the original engineers on the EVI MCS 100-3 and he remembered that these units were programmed that way to get around a bug that was discovered in the Honda EV Plus. The bug was that one of the computers in the Honda EV Plus would stay on and listening to the pilot after the charge cycle was complete. This listening prevented the computer from going to sleep and it would continue to draw power from the 12 volt system on the car until the pilot was removed or the 12 volt battery was dead. Having to jump start your electric car just because you left it plugged in would not be a happy experience. So the initial solution was to have the pilot shut down in the EVSE after one cycle. I believe Jason did mention he was instrumental in getting the bug fixed in the Honda EV Plus itself but of course this single cycle behavior is still built into my EVSE. I was also told that this EVSE is still fully J1772 compliant even with this single cycle behavior.
It seems that the hardware and software used to program the pilot in these units is long gone so removing the single cycle behavior from the pilot controller does not seem feasible at this time. Jason did suggest one thing to try and that was to momentarily disconnect the pilot line while the LEAF is plugged into the EVSE to try and fake out the pilot into resetting the cycle without the LEAF noticing but the LEAF would just trigger a cycle again no matter how fast I did it.
So at this point I am going to try and see if the LEAF timers at least have a small window after they trigger to get the car in and still have it charge. This way I might be able to get the pool timer synchronized enough that I will be able to join the 80% club.
It still boggles my mind as to why you can't set an 80% charge without a timer.