Low-level calibration must be run completely in order listed in SM, otherwise meter will become upset and reject new calculated values. That's why I couldn't calibrate 2001 before without actual 5700, even though I could run comprehensive cal for 2V/20V/20K/1Meg. But that does nothing for current ranges, so not enough
I'd say easiest for hobbyist is to read and decode calibration ROM format with constants (you can read floating values by :CAL:PROT:DATA? query over GPIB, but can't save to cal rom).
Calculate values, correct checksum and then write calibration ROM back to meter by external I2C programmer (I've used TL866 with sucess on my 2001s/2002, however I just read/wrote cal dumps when swapped analog boards between digital boards, didn't modify them).
But I doubt you get much improvement to justify the effort, as even if you leave meter run for few weeks, it will already drift few ppms here and there (still within specs), so it's bit much to expect ppm-level accuracy from 6.5d or 7.5d meter