Thanks for sharing. If I use 0.1% shunt resistors, and hand select the LM317, I might give this a shot. I could use a larger voltage if that would help, say 7.5 or 9v, perhaps lithium chemistry...Separate from that is the 317's initial voltage tolerance. This is the variation in the internal voltage reference over the operating temperature range and from one chip to another. The datasheet says it is +/-4% over temperature. It also says the output regulation error can be over +/-1% on top of that.
If I buy a few dozen LM317 to hand sort, which manufactures should I choose, Texas Instruments , STMicroelectronics, onsemi, Analog Devices, or?