Just as a follow-up for anyone else out there with the same problems, this 
is what I did to "fix" it:
BasicRender worked better than FastRender on animations, but FastRender did 
a better job on keeping object faces "solid", so in my environment class, I 
switch between the two as necessary.  Also, FastRender does object sorting 
using the screenZ property, so I overrode the built-in calculation and 
manually sorted the objects on my own.  This created a problem with complex 
objects, like one partially inside another, so I created a separate mesh 
with the two objects joined as one, and use the separate objects for 
animation and switch to the single combined on completion.  Also, I used the 
mesh sortType (which defaults to center), to switch between front and back 
depending on which method sorted which object faces better (large objects 
with large faces worked better with back, and small objects worked better 
with front).  Additionally, since this specific application didn't require 
user manipulation, just built-in animations, I was able to use perspectives 
that were advantageous to me and gave the "correct" view I was looking for.  
Finally, I applied a WireframeMaterial to the objects for development and 
placement, because that allowed me to get precise positioning over the 
objects as the textured object could give misleading results.
All in all, I was able to get satisfactory results both for myself and the 
customer.  If anyone else has additional comments or tips, I would still 
appreciate them.   Now to rebuild it all in Broomstick.....

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