I've never made ice cream but my first thought on reading your post was that it would make sense to start with an ingredient that's already fairly thick and creamy, such as crème fraîche.
Looking on the BBC Good Food site for a suitable recipe found this, which has loads of 5 star reviews (and where several people have specifically commented that the didn't experience the usual problems, e.g. with ice crystals, that they'd associate with making strawberry ice cream).
Worth a try, perhaps?
https://www.bbcgoodfood.com/recipes/590633/strawberry-crme-frache-ice-cream