You are correct it is all about context i.e.
Ní mór an cat a chur amach; It is necessary to put the cat out.
Ní mór den bhia a d'ith sí ; She did not eat much of the food
an alternative I use is = ní foláir One nust/It is necessary
The only small difference in my experience with Irish here would be:
Ní mór den bhia a d'ith sí -- sounds very odd to me!
Ní mórán den bhia a d'ith sí,
Níor ith sí mórán den bhia
'mórán' being a sort of 'strong' word the emphasis is there anyway.
You can also have:
Ní mór duit a bheith cúramach = You must be careful
I might suggest that probably the best way to get away from the 'negative' thing with 'ní' in the mind in this usage is to learn some samples 'off by heart' and when repeated enough, they will become natural and can be more easily applied to other situations.