That looks fine to me too.

I wonder if the difficulty they are having is not surface sectors per se but the "stopover in the continent of origin" rule. They may be counting three (PEK, SIN, HKG) but in fact a surface segment is only one stopover not two.

All the versions of the rules I know now say explicitly that a maximum of 20 flight segments are permitted, so the surface segments taking it over 20 in total isn't be a problem.

The other difficulty they will be having is that the ticketing system may require an extra coupon for the surface segments which means this is going to require 6 packs of coupons (I believe they still come in fours even with ATB tickets). This may be more than some system somewhere can cope with.

But in any case, persevere - this is a perfectly valid itinerary.