Seems like you are missing the point. The R2400 is miles ahead of the 2200. If you really want to cut ink costs get a 4800 and forget all those silly work arounds.
Care is needed discussing this subject. There are three variables worth considering when evaluating the cost per cartridge: (i) amount of ink in each cartridge (is it the same for both printers?), (ii) the amount of ink required for a print (may be less for K3 inks in a 2400 compared with Ultrachrome in a 2200) and finally and (iii) the quality difference. What matters isn't the cost of a cartridge, but the cost of the ink used to make a print and the quality of the print - as for the latter, if you are producing colour prints on matte paper, the difference between the 2200 and the 2400 is a slight saturation boost from the 2400. The real advantage of the 2400 shows in producing B&W prints and prints on non-matte coated media. There is a noticeable improvement, but not to turn the world upside-down.
As for buying a 4800 - yes, the cost per ml of ink is much less, but the machine is far more expensive to buy. A purchaser needs to consider essentially two variables in making this decision: (1) whether the volume and size of prints to be made justifies the large cost premium and (2) whether a RIP will be used. For large volume, large size prints, or for using a RIP the 4800 makes sense, and these factors are likely more important than the ink cost difference. When you buy a 4800 you are also buying a commitment to keep using it frequently in order to minimize the cost of print-head cleanings.