Ours were 9 months old and we didn't hang them at all. The only info I could find was about wildfowl geese which are hung, perhaps because you can have no idea of their age. We have roasted one and the rest are still in the freezer. I did a very slow roast in a covered roaster and it was totally delicious, far more so than I expected.
For your older one, probably yes, hang her for a few days. I wouldn't waste a goose on curry, but a red wine casserole, with an orange added for sharper flavour, sounds perfect. Don't forget there's quite a lot of meat on the back too, fine for a stew.
You could also take off the skin, which would otherwise make the casserole horribly fatty, and roast that separately for a 'pork scratchings' style snack. Oh no, I've just remembered you're not plucking them.
I don't know about gutting or not, but I would keep them without food for a bit before slaughter if you're going to leave the guts in.