How to measure output voltage of this Li-Ion battery circuit?
I would make another measurement at the transistor drain and subtract and subtract.

A MOSFET is not like a mechanical switch; it is not simply "on" or "off". The drain-source voltage depends on the magnitude of the voltage on the gate as well as the drain current. The datasheet probably provides graphs of this relationship, but only the typical characteristics will be shown. The datasheet probably will not provide information you can use to accurately predict the drain voltage...there is just too much variation in parts.

By the way, you have two resistors marked R1 in your schematic...how does that happen?