I have been trying to make ice cream with sucralose. So far all I get is just a hard rock after tossing it in the freezer. when I try to thaw it, it goes right back to a liquid. I'm not very confident in trying to use eggs in this. I have tried in the past and it didn't come out well.
The sugar in ice cream isn't just there for the taste, it also has an important effect on the texture. Ice cream isn't a pure compound, and doesn't have a single fixed melting point but a melting traject. The more dissolved solids (sugar) you have, the longer the melting traject of the ice cream. It also starts to melt at a lower temperature.
That translates to a softer icecream (when it's stirred enough while freezing to avoid large ice crystals). When made correctly and served at the correct temperature, a sorbet isn't fully frozen.
When you use sucralose, you need a lot less for the same sweetness, and thus you end up with less dissolved solids. That means a higher melting ice, which is a lot harder at the normal serving temperature, and which goes straight from solid to liquid.
This is for sorbet type icecream (basically fruit and sugar sirop, with some extra ingredients to adjust the taste). When you make milk or cream based ice creams, the basics stay the same, but the extra fat helps getting a soft and smooth ice without large water crystals. If you insist on using sucralose or other artificial sweeteners, you could try starting with a custard base (traditional custard, from cream and egg yolk), and replacing only part of the sugar. Industrial ice creams include some ôlysaccharides to improve the texture, but those might be hard to get for home use, and have to be dosed rather precisely (and in small quantities).