That bobduino thing looks pretty cool. I've also seen a similar thing that was just shift registers, I think it was 8 of them, I cant remember for sure.
I have been working on documentation for 3 different RGB LED cubes, they all controll 64 RGB LEDs, but they do it 3 different ways.
I still have a lot of work to go, I have one cube up, and details about how what wires to use, how to prep them, and why.
I really think the split is a bad idea, It will require some kind of non-conductive structure in between. I dont see any good way to do this, it will only make things harder, and I think the results will be less than desirable.
I have seen carbon fiber tubes and plastic stuff at the hobby store, if you really must try some kind of non-conductive alternative, you might find something there. What you will find there is something called music wire, its hardened steel wire, and is very very stiff. Its harder than hell to solder too, but it provides a really sturdy structure, that will flex a bit, instead of bending and kinking. You can get very thin wire, that is stronger than bailing wire, and much much thinner, and harder to see.
You should really learn about Serial communication, like I mentioned in my other post. Transmitting the data (64 bits per plane most likely) Since you do not have 64 pins available, there is no way to do that with parallel, so you will need serial, there is no doubt (unless you were willing to entertain charlieplexing...) Since you are forced into serial, you really wont need a mega, but it has more memory, so that will be useful, but you really only need a few pins to do serial data transfer. Since you have so many pins available, you may elect to use one pin per plane, and 3 pins to serialize your data through. Since you will be doing some form of serial, you have lots of options, shift registers, LED drivers, you could even do a ton of resistors and transistors. Drivers come with a lot of different features, I've tried get my head around what things are important, and its confusing.
If you go with a constant current driver, like the TLC 5940, you can do it with 4 chips (each chip is 16 bit, and does PWM), You will need to source current to each plane, as the TLC chips are sink only, no sourcing.
If you use shift registers, the nice thing about them is that they can sink or source, so you could source using a shift register, and sink with something else. The downside is that they dont control the current, so the will need resistors.
Multiplexing chips probably wont work for you.
I havnt finished my higher power cubes, but you will need to sink or source current to your planes, I've done a little reading and it seems there are 2 common ways to do that, darlingtons or mosfets. Mosfets are preferred as they seem to be more efficient, especially when not being used (and your mosfets would only be used 1/8 of the time).
The current website im working on is about RGB charlieplexing cube, but you will find some useful info about building cubes in there. I would strongly suggest building a couple small structures with just a few parts, and actually complete something so you understand all the steps before you try to design your own process.
The most realistic way I can see building this cube is 8x64 setup, and common anode(planes) is the most versatile way, since you could use shift registers or constant current drivers.