For the ice cream: Place a metal loaf pan in the freezer to chill.
Using a spoon, remove the solidified cream from the top of the coconut milk, leaving the coconut liquid behind in the bottom of the can. Place the cream in a large mixing bowl. Add 1/4 cup agave, then beat with a hand mixer until soft peaks form, 2 to 3 minutes. If the mixture is lumpy, add a little bit of the coconut liquid from the bottom of the can.
Combine the tofu, cocoa powder, coconut oil, vanilla bean paste, salt and remaining 1/2 cup agave in a blender and blend until smooth, about 2 minutes. Pour the mixture into the bowl with the whipped coconut and fold until combined. Transfer to the chilled loaf pan and place in the freezer until firm, 4 to 6 hours, or up to overnight.
For the mixed berry sauce: Add the berries, agave and lemon juice to a medium saucepot over medium heat. Bring to a boil, then reduce heat and simmer until it starts to thicken, 5 to 7 minutes. Remove from the heat and add to a clean blender; blend, making sure to remove the center of the blender top, for about 30 seconds. Pour into a heatproof container and let cool slightly before serving, about 15 minutes.
Scoop the ice cream into bowls and top with the berry sauce.
When blending hot liquid, first let it cool for five minutes or so, then transfer it to a blender, filling only halfway. Put the lid on, leaving one corner open. Cover the lid with a kitchen towel to catch splatters, and pulse until smooth.