How did this go?
I’ve been trying a bit of grdvolume lately, and it looks like it does not take into account slope:
$ gmt grdmath -I1 -R-100/100/-100/100 X = tri.nc
$ gmt grdvolume -C0 tri.nc
0 19999.96 999996.020931 49.9999010464
Which is roughly equal to A = 100*200 = 20.000.