Having a few IO pins in a connected state might add 5-10uAs. The changes in the code which removed all the pins from being INPUT by default saved about 500uAs.
Looking at the HX711 library, there are power-up and power-down methods. I don't see these being called anywhere in your code. Ideally, you should power it up just before the reading and power down right after. You may need to see if there is a warm-up time required after powering up before a reading can be taken. According to the datasheet, it uses about 1.5mAs when in the powered up state and about 1uA when powered down.
I'm not sure how you were getting better performance with the Mbili, unless your sleep code for the Mbili also makes a call to power down the HX711.
I curious what the output range is from the load cell. The Autonomo can set its ADC to apply up to a 16x gain with a 12bit resolution.