It must be the as you described. There seems to be some difficulty getting the signal to latch in the shift register. Is there an easy place to monitor this process? My hands are not that steady to monitor the surface mounted chips.
I have been able to get an output to 24VAC, but its usually not the expected one and I usually cannot get it to turn off when I do get it turned on. So that seems to add to your theory about signal difficulties.
On a positive note, I did get the RTC clock working reliably:
$ sudo hwclock -r
Sun 14 Apr 2013 18:58:44 UTC -0.425368 seconds
so at least the I2C bus is working correctly.
I attached 2 pictures. One with it all together and one with them separated. I turned it off when separating them.