Full charge on these is 1.2V. Going down to 1.1V seems like it shouldn't hurt them that bad.
No, 1.2V Ni-MH battery has full charge voltage at about 1.4-1.5 V.
Full discharge threshold is at 0.9 V, but its going very fast from 1.0 V to 0.9 v (about several seconds), and it's not recommended to discharge it below 1.0-1.1 V.
At 1.1 V it remains about 5-20% of charge, depends on battery model.
At 1.0 V it has 0% of charge.
Here is EMF voltage vs residual charge curve for Ni-MH:

But note, full charge voltage for Ni-MH depends on exact instance of the battery, you're needs to check -dV/dt event to stop charge, do not use voltage for that.