Reading your plans about cutting rounds after baking, leads me to believe you're looking for the sort of sponge cake which comes pre-packaged at the supermarket, rather than an actual short cake -- which is more like a biscuit with a little sugar in it.
If you want a recipe for the latter, I'll be happy to do it for you; but it's pretty much "biscuits in your usual way; but with a little more shortening; 1/2 and 1/2 for the liquid; add 1/4 cup sugar per 2 cups flour; and make them thinner and wider than usual." As a cooking teacher, that probably gives you more than enough to go on.
A Bisquick variant would be 1/2 and 1/2 as the liquid; add 1/4 cup melted butter and 1/4 cup sugar per 2 cups Bisquick; and, again with the thinner but wider.
If you like, you can pat the disc out, lightly flour the top, and do three to five turns -- that will make the biscuits more "flaky" and layered. Don't worry about the turns; any biscuit can take a few, and short-bread biscuits are even more resistant to overhandling.
As to the spongey type, they're not so much short-cake as Mary Anns. If you don't already have a recipe for a dense sponge, Mary Ann type cake, there's a good one here: Diana's Desserts Forum - making a cake more dense
. I doubt you'll have much trouble adapting quantities or from Mary Ann to sheet pans. By the way, butter your pan heavily to get the right texture and color on the bottom of the cake.
Good luck finding good berries,