Ok, slight problem.
I just finished all the main circuitry for the build with only the incandescents left to wire up.
I've been running my example sketch throughout the build, it ran through each segment's output one at a time with no problems.
Now here's the problem I was worried about, I edited the sketch to turn on each output one at a time with an interval of about 200ms. After a very brief time with all 28 I/Os on, the 5v regulator overheats and shuts down. 
I figured that the problem could very well be because I'm running the poor thing off Arduino's maximum rated voltage of 12 volts. So I swapped the 12v supply for a 9v one. Results were better this time in that it did not overheat as quickly, however I shut it down after I clocked the PCB temperature underneath the regulator at a blistering 185F (85C). I don't really have any wall power supplies under 9v, nor would I like to use a second one next to the already necessary 12v one, so I'm now wondering if there might be an alternative regulator I could use that would accept the 12v input.
On the other hand, the ATmega2560 seems to accept the LED and opto load just fine.
Edit:
I just found myself a regulated 5v power supply. I paired it up with the 5v rails on the Arduino and everything seems to be getting along just fine... For now. 