What is the best way to solder a large flat SMD shunt resistor so as to minimize joint resistance?
This type of circuit would generally use a 4 lead shunt resistor, these break out 2 pads specifically for measuring current, in your case, you could fit bodge wires to the top of the resistor, this will remove more of the offset, but it still will not remove the issue completely. 



Image source is from a supplier, so not sure how to handle that with the size rules