Compared with the "traditional" forced carbonation method of big CO2 tank + regulator, the straight dry ice method has two problems.
There's no way to control the pressure over time. You can drop ice in there one, create some pressure, and after a while the CO2 will absorb into the beer. Then where are you? You've got 4 grams of CO2 dissolved (question: does CO2 dissolve or mix?) in your liquid, another 8 grams sitting above the beer at like 30 PSI, and no more dissolution is happening. Well, there might be dissolution, but it won't be what you want.
Also, there's no way to regulate the pressure. If you accidentally drop too much in there, if the yeast create some CO2 themselves (thereby screwing with your calculations), or if you want to add more dry ice later in the process (after some carbonation has already taken place), your math no longer works.
You can solve the second problem rather easily: Just get a pressure release valve (idea credit: Brendan, of course), set it to something reasonable like 60 PSI, and drop as much dry ice as you want into the beer. Cap it, and let the regulator prevent explosions. God only knows where to find said regulators, but they must exist... somewhere. And if they don't? Well then we'll figure out how to build one.
The former problem is a little harder. You've got a few choices.
You can just ignore the problem. When you want to add more dry ice, just do it: Open up the keg, drop more dry ice in, close it again -- pressure loss be damned. Note that this necessitates the existence of the pressure release valve mentioned above, because your math is going to be Wrong (with a capital W) no matter what. You could also build yourself a little pressure lock chamber. You open the top, drop a piece of dry ice in, close the top, open the bottom and allow the dry ice to fall into the beer, and then close the bottom again. You'll lose a slight amount of pressure, but assuming constant temperature and a pressure measurement, you could do the math and not kill yourself.
Barring all of this, you could do what root beer and sparkling water makers have been doing for a while: Grab a big hunk of dry ice and drop it into the beer. Keep the lid off the keg and let the dry ice boil. After the sublimation stops, cap it and let it sits for a while. The only problem with this is that the starting temperature of the beer will drastically effect the absorbtion of CO2 into the liquid, even over a relatively long period of time. Additionally, it is unclear from online resources how effectively this really is at carbonating beer. It might be fine for carbonating a heavy stout, or a brown ale, but we doubt that it would carbonate a good lager or blonde effectively.
I'm going to be transferring scads of beer this weekend (alone!). Once it's kegged, I'm going to steal one of the kegs and see what I can do with this dry ice stuff.