It all sounds good Raggytash. But I wonder if it might be prudent not to let your cats out at night, if they would tolerate being locked in until the morning? If they go outside, the Monster may attack them in your garden, and they may sustain wounds before they can rush back in through the electronic cat flap.
It's all most annoying I know.

Steve, I'm so glad you and your wife are persevering with putting out food and trying to help the little abandoned cat. Now things are thawing out, the food won't freeze solid and if the cat is quick, he/she can get it down them before other creatures get a look in (foxes, rats etc) I reckon cats find us, and this one's for you I think!