Unfortunately yes, you cannot do the CX/VN codeshare. However, maybe you can fly to BKK and then buy a BKK-Vietnam sidetrip. The fares BKK-Vietnam are quite competitive (at least to SGN) as many airlines offer Fifth Freedom Rights as an ending from their European - Thailand flights. AF, LH offer great fares in addition to TG and VN of course.
Remember than the GlobalExplorer is a mileage based fare and you're only allowed up to 15 stopovers max.
Maybe you'd like to try Star Alliance instead for the route TG to SGN SQ to SIN?