Hi Paul,
thank you for your posting! I am sorry, my topic is a bit complicated. I try to explain it.
Besides the other alternatives, with the configuration where the latch is permanently tied high and the Output Enalble is tied low, I tried to test the shift registers. I wanted to see if they are getting the bytes in right manner.
At my fitst runs, I tried it the normal way with latch only high when data is coming and OE high when the outputs should be active.
But it also did not improve the intensity of the LEDs.
I would love to use the MAX7219. I even bought one to test it. But the problem is, all LEDs are common Anode.... 
Data Sheet MIC5821: http://www.micrel.com/_PDF/mic5821.pdf
Data Sheet MIC5891: http://www.micrel.com/_PDF/mic5891.pdf