I had your same problem with my 34901A. I almost never use the current channels. I use one of the voltage channels with an external shunt and the math function to display the value scaled in amps.
The 34970A uses a 0.1Ohm resistor for the 1A range, and 10Ohm for the 10-100mA ranges. The 0.1Ohm resistor is nothing special.
What level of accuracy do you need? I use a 0.2Ohm 5W 20ppm/°C up to 4A or a 1Ohm film resistor for lower currents (consisting of multiple resistors in parallel).