I don't have an DSi XL, but checked the resistors again on my normal DSi. Measured in one direction I am getting around 14.5Kohm, but when swapping the pins I am getting 17.7Kohm. Apparently there are some electrons flowing through the attached chips. 17.7K should be more accurate, but it might still have the same issue, so real value might be 20Kohm or even higher.
270 ohm sounds almost definitely wrong, that would give you lots of Watts for a pullup resistor (from my experiences pullup's are usually in 3.3K .. 33K range). Checking two Samsung datasheets: KMCEN0000M-S998000 recommends 50K .. 100K, and KLMXGXFEJA recommends 10K .. 100K, for the eMMC Data lines. With the big XL case, you could probably attach a small circuit board with some solderpads somewhere, wire it to the datalines, and then wire normal non-SMD resistors to the solderpads. I would try something like 20K, 33K, 50K (and check if you get 14K one-direction and 17K other-direction after connection, if so, then you've probably found the right resistor).