If you do find that this is a useful method (perhaps when the throughput and SED are generic functions, rather than tabulations), then it's probably worth getting the more complete sets of coefficients from GalSim/include/galsim/integ/IntGKPData10.h.  It starts with the 10 node Gaussian quadrature, and then does Kronrod and 3 more Patterson steps, so you don't need to restart the adaptive process as often.  That's the basic method I used for `int1d`.

But like I said, I don't expect this to be a good choice for the integration technique when using a tabulated function, so it's probably not worth spending time on now.  We can wait until there is a use case that would be improved by having good GKP integrator that acts on images.