Many professional bakers put the strawberries in the filling/frrosting, rather than the cake, probably with good reason. And I have used the Cake Bible’s strawberry puree, thickened with gelatin, as a filling and it was wonderful- very fresh, light, yet intensely flavored. Perhaps your little one could be convinced of how nice it would be to have pink or red stripes in the cake (buttercream, cloud cream or thickened puree between layers)? If so, my thought would be to use either the sour cream butter cake (light and fluffy) or the golden butter cream cake (denser but a great partner with strawberries) and then torte/fill the cake. You could also arrange fresh cut strawberries in a large flower on top of the cake.
Here’s a recipe from a forum member for strawberry muffins, would your little one be interested in cupcakes made from these? http://butteryum.blogspot.com/2009/02/strawberry-muffins.html You could still frost them and decorate as for a birthday, and if you arrange them on a tiered stand they will be very festive. It might save you having to bake all those test cakes. :)
I also saw a cake in Dede Wilson’s recent birthday cake book that has raspberries suspended in it, perhaps that might work for strawberries as well (though I think the strawberries have more water): http://www.realbakingwithrose.com/2008/10/dede_wilsons_new_book.html
A few thoughts on your questions:
1. USDA nutrient database: http://www.nal.usda.gov/fnic/foodcomp/search/ and http://www.nal.usda.gov/fnic/foodcomp/cgi-bin/list_nut_edit.pl
2. Milk/sour cream. However, keep in mind that with chunks you’re not trying to adjust for all the water in the berries, just the amount that will leak out into the batter as they cook.
3. I would be tempted to try to leave the sugar alone, as the berries won’t be as sweet as the rest of the cake.
4. I would imagine that it’s better to keep the pieces small/lightweight so as to not sink in the batter. Puree mixed into the batter would need to have all the variables accounted for: water deducted from milk/sour cream, fiber possibly deducted from the flour, sugar deducted, and acidity neutralized by substituting a little baking soda (1:4) for part of the leavening.
5. Perhaps the sour cream butter cake, as that batter is pretty thick and might give a little extra support to the heavy berries.
6. Probably, there are a lot of variables to work out! :)