If you are drawing enough juice with the ice, then the alt can certainly expire very quickly, as a rough rule they will only give out continuously around 1/3 to 1/2 of their rated output, which is a peak, which can be as brief as less than a second.
In short if using loads of ice, think about additional battery or alt upgrade.
Loads of different ford fitments ones will fit, they can also be spun round 180 if they are the wrong "hand" side.
tabetha