I have the cuisinart too! I actually bought it to make Keto ice cream. We let it run for 25 mins minimum, never less, usually 30-35. Once I went for 40 mins max. It is harder to scrape off the sides when I run it longer because it freezes solid to the edges, and I have the newest one that is supposed to scrape the sides while churning. Gimmick sort of. It’s not as bad as the older version but a thin layer still freezes and the beater doesn’t keep that from happening.
The very first time I made Keto ice cream two years ago I made it with Allulose. Since i was new to Keto and all these new ingredients and sugar subs, I was in the bathroom for several hours after eating 1/2C of the ice cream. 
I never used alluloae again and switched to powdered erythritol and powdered monk fruit as they had less impact on me. However today my body is more tolerant of Allulose and I started using it again but in smaller amounts.
You could use regular milk but higher sugar/carb content. I’ve tried many, many ice creams using different “milks” like heavy whipping cream, almond milk and coconut milk and coconut cream (both from cans, Thai Kitchen, because it tastes the most authentic like how I had it in Tahiti.) I have found heavy whipping cream was the tastiest right after the machine was finished. That’s the best time to eat it.
What I haven’t figured out yet is how to not get it to freeze rock solid in the freezer. I see all sorts of videos and recipes online boasting scoop-able ease, and I swear they are ALL lying just to get traffic. I’ve tried adding the vodka to keep it scoop-able, but even that doesn’t work. I would love to know how to make it scoop-able after frozen. But until then we only eat it right after we make it now.