So, I made a grid in photoshop and played around with various dimensions - sending the image back and forth from my computer to my Nexus 10 - and found some dimensions that work perfectly.
Basic
Width: 1940 px
Height: 1250 px
Resolution: 72 ppi
Of course we have to take into account the N10's awesome resolution of 2560x1600, which equates to resolution of 299 ppi. Thus, keeping the aspect ratio the same as above and setting the resolution at an even 300 ppi, we get the following:
Width: 8083 px
Height: 5208 px
Resolution: 300 ppi
[Edit 11/24 - at a reasonable hour in the evening]
I don't know what I was thinking at 3am when I posted the above, but that resolution is outrageously large. Guess what happens when you scale the size back down and keep the same aspect ratio! You get dimensions of
Width: 2560 px
Height: 1650 px
Resolution: 300 ppi
Duh!
So after all that, all there really is to conclude is that you can design your backgrounds for the exact dimensions Google has advertised. It will still account for the scrolling and will fit quite nicely. I would only note that a height of 1650 seems to fit slightly better. As far as resolution goes, go with whatever you feel is best. IMO, 72 ppi is too low (background seems a little blurry), and 300 ppi is probably too high and creates an unnecessarily large file size. 300 ppi is usually reserved for printing, not computer displays. I would recommend you find something in between that works for you.
Now go design something cool!
-Aaron