OK, I think perhaps I've got my finished layout, unless anyone has a pressing error.
Here are the most recent changes:
-Swapped capacitor packages to align with Mouser components
-Moved LED driver ICs under LEDs themselves
-Made most resistors vertical where prudent
-added a debug LED (with 500 ohm resistor) to an output pin for Atmel debugging
-Added a 2x2 header for added functionality
-tied Iset (each max7219) to VCC instead of GND!!
-moved screw holes around for better positioning
I took melka's advice and placed the driver ICs underneath their respective displays. I'll use regular female header sockets to elevate the displays, and then install the ICs underneath. You'll note that each max7219 driver has an electrolytic capacitor below which will not fit vertically (they're 11mm tall) so I left room to lay the caps on their sides. And you're right, with the displays sticking up higher it will be simpler to make the case's front panel fit better.
melka, I didn't understand what you meant about the 7219's minitauresque wiring. I'm pretty sure that I have done the bare minimum of wiring to get the displays setup correctly. My question is.... will it work how I have it wired now? (Again, I did update Iset to be pulled to +5) Right now there are three outputs from the microcontroller: Load (CS), Clock, DataIn. I don't believe I need any more...?
At this point I'll shoot to send in the CAM files for Wednesday morning, unless anyone can point out more serious mistakes in my layout or schematic. Once more, thank you for your time! I have since found several mistakes that really would have kept the board from working.
Oh, and the purpose of this board: This is a tool called a "Digital Readout (DRO)" for a metalcutting lathe. It takes a BCD waveform from Chinese linear measuring scales and outputs the current actual position onto the 7-segment displays for both axes. I have a thread going on a machining forum about it here: http://www.practicalmachinist.com/vb/showthread.php?t=176632
Once I was able to read the data from the linear scale and see an exact position on my serial port, I decided to go ahead with the PCB because everything after the data input is definitely possible.
Thanks everyone, Andrew