Selu seems to stabilize well with a gain of 0.75:
in: 1.0013
out: 0.7974 grad: 0.6252
out: 0.3138 grad: 0.2894
out: 0.2418 grad: 0.2414
out: 0.2097 grad: 0.2160
out: 0.2118 grad: 0.1993
out: 0.1939 grad: 0.1985
out: 0.1909 grad: 0.2259
out: 0.1849 grad: 0.2329
out: 0.2048 grad: 0.1998
out: 0.2060 grad: 0.2007

But I’m not sure why 0.75 is magic here or whether the scaling of the Glorot initialization achieves invariance under the layer size.
My takeaway was that there is a fixed point and I’m reasonably happy to try to find it myself. But don’t take that as advice, I am just a random clueless guy on the internet.
Best regards
Thomas