Updating MRW (1992) with PWT 9.0
Your assumptions seem correct. For savings rate, the consistent definition with MRW would be

$$ \frac{ccon - cda}{cgdpo} $$

ccon is domestic absortion, equal to $ C + G+ I$, whereas cda is $C+G$. Therefore, $I$ is investment, which by definition includes both private and public sector.