I've done something similar but pricing out the stopovers (with same routing as my ticket) not each segment. Got me very close with some important differences vs point to point. There is usually only 1 YQ charge for multiple connections which makes a big difference when you connect on two flights with large YQ.

E.g. GRU-DFWx-NRTx-SIN has no YQ if straight through, and plenty if it were as stopovers. The reverse does has YQ (~$200). This can effect your routing quite a bit if you care about YQ and are happy for long flights connecting to long flights.

Last XMAS/NY (somehow now 7 months ago!) I spent a few hours doing and recording lots of these with the intention of a post with an overview. Minded to go back and update/finish that at some point, brought up some interesting quirks. I did get a bit confused by BA charges, turns out I'd stumbled across the no YQ within continental Europe change.

You get to see some interesting carrier politics hinted at in the YQ charges. E.g. BA shows up as ruling Europe as I assume they pushed for basically anywhere in Europe to the US to have the same YQ. JAL seems to have won a concession such that "its" YQ is charged for DFW-[NRT|HKG]x-SIN which makes DFW-HKG-SIN cheaper buy enough to pay for a night's hotel in HKG IIRC.