Variance, the circuit for each strap is simple, it's either a pull up or pull down for each nibble.
Let me make this clear as many people have missed this, there are two possible resistors for each nibble, one pulls up, one pulls down, only one from factory will be populated, the other unpopulated.
1) Use ohms on you meter to figure out which pads are ground, take a photo and note them all (I just put a colored dot on the photo)
2) Use ohms on your meter between the VCC pin of the EEPROM and the pads to figure out which are VCC and note them all (again, just a different color dot).
3) Now you need to identify which positions are common for pull up/down, so again on ohms, measure between the pads that are still unknown looking for two that are connected.
At this point you will have a good idea of which resistors are worth looking at. To discover which is which, since the nibble is changed every 5K, solder a 10K resistor over the already existing 10K resistor to test, this should change one nibble as it will drop the resistance to 5K. If it doesn't work, its not the right resistor.
Once you have identified the resistor for each nibble, and know which set of pads are for the opposite (pull up/down), you can then figure out what needs changing. Some resistors may need swapping with different values, depends on your target ID. Others may need removing and populating the other set of pads for that nibble to pull it in the opposite direction.
From factory none of these will be floating, you should not have more or less resistors on the PCB after you have done your mod, if you have, you have done it wrong.
Leaving a resistor off will cause the input to float, and the nibble ID will be undefined, it could change from boot to boot causing you odd problems.