I'm not sure what you're finished ice cream product looks like, so this answer is based on conjecture, but I do have a few recommendations.
I think the main issue here is that the recipe calls for too much sugar. If I were you I would reduce the sugar to about 3/4 cup. Large amounts of sugar drastically lower the freezing point by interfering with recrystallization during freezing. This would explain why you are unable to get the soft serve consistency that you are looking for. It also explains the lack of creaminess because the ice cream is not able to freeze around the air, which is where the volume and creamy feel come from.
If that doesn't work, then I second the notion to try an egg custard base or to add more cream, but honestly it looks like the recipe already has plenty of fat. Altering the fat content could be more damaging to the recipe because the proteins in dairy are essential to stabilizing air bubble formation in ice cream.