and it seems like the sh1OH1 has made my output signal hotter than his.
That is not possible.
There are of course variations between different SH-101, some caused by age, other by tolerances.
Some of these variations can be corrected via calibration, other not.
btw. your rand waveform bleed could be caused by dirt or grease on the pcb below the sample and hold capacitors of the DAC.
But no way to tell from here.