Doesn't volume matter?
I would think it would take longer to saturate a larger volume of liquid with CO2.
I should have paid attention in Chemistry class.
Don't worry, this stuff isn't taught in chemistry classes! It's taught in transport phenomena class if you're a chemical engineer though
The volume relative to surface area is what matters, not necessarily the volume itself. By using a carb stone or shaking the keg you expose much more of the beer surface to the gas inside the keg, making it come to equilibrium faster. That's because the gas is diffusing into the liquid at a fixed rate along the beer-liquid interface, so the bigger that interface is the more gas can diffuse.
You can also speed up the diffusion by bumping up the pressure, but as Topher said that generally gives inconsistent results. Just set it to your carbonation pressure (which in a balanced system is the same as the serving pressure), wait a few weeks, and you'll be good to go.
CO2 pressure and dissolved CO2 concentration are very much analogous to heat and temperature.
Think about it like cooking a turkey in the oven: You ultimately want the turkey to be at 160 degrees. You could do this by cooking it for a few days with the oven set to 160 degrees, and it'll be impossible to overcook (not that this will yield a tasty bird, but ignore that for this analogy

). This is analogous to the "set and forget" force carbing method. Or you can set the oven to 400 degrees and cook it in a few hours, but you risk overcooking it if you don't time it perfectly. This is analogous the "burst carbing" method.
It takes a while to cook because the heat is diffusing from the hot oven into the mass of cold turkey. The heat can only diffuse in at the turkey/oven interface, so cooking time is really a function of surface area, not weight. This is why old school cookbooks that say "cook it at xx minutes per pound" are usually wrong. You can speed up the diffusion of heat by turning up the oven temperature or increasing the surface area.
So if you cut the turkey up into legs, thighs, wings, breast, etc. you'll increase the surface area, which will let the heat enter a lot faster. This is analogous to the shaking the carbing keg or using an aeration stone.
