OP you likely wont find SG, SH or SJ spec oils as those were superseded years and years ago. By memory the latest is SN. You will find SL and SM spec oils and these are fine (actually better - they have improved additives, better sludge control, etc etc)
If anything, end of the day the Ecotec will almost run on cooking oil - they are very non-fussy. As a reference though, my partners VY with 270k on it has just been changed to 5w40 Shell ultra, after running whatever quality syn 5w30 or 5w40 oil is on special for the last few years. Still runs beautifully, is very quiet and I would hazard that I top it off about 500ml over 10000kms between changes.
I would only step up to a 20w50 if it had oil usage problems. The old Aussie "thick is better" 20w50 attitude comes from the 80s when it was pretty much all you could get. Compare that to the yanks who also had this engine and happily used 5w30, 10w30 with no issues (and likely had better economy from using it)