Most nights of the summer, we make ice cream in a Donvier churn (no ice needed). Over the season strawberry, mulberry, juneberry (Amelanchier), blackberry, gooseberry, blueberry, peach, black rasp, red rasp, pawpaw, chinese che (Cudrania), fig, etc.
Fig has been our least favorite.
My 12 yr-old son likes strawberry and juneberry. For intensity of color, I like mulberry and Chinese che. For something different, we enjoy 'Invicata' gooseberry. With it's thin skins and green fruit, it reminds me of lime ice cream. It's sweet/tart balance works nicely, perhaps similar to your cranberry experience.
To use copious pawpaw fruit, we combine 1 part fruit to 3 parts Jersey milk. Mush in, mush out!
Heron, as for black currants, there is a range of fruit available, with a range of "off" flavors. Could you share which black currant cultivar(s) you used for the ice cream?