I’d suggest the following for the female header:
517-929984-01-20-RK or 200-SLW12001TS
These expect a standard square(ish) pin header rather than the precision pins (round). Thus you can use standard pin headers for the male side.
Looking at the datasheet it seems the only difference is the “Plating code”? 83 vs 87. I’d also be confused as to why that would not fit as expected.
SS-120-G-2-N may be an equivalent substitution, but triple check the data sheet