I would like to make this recipe into a sheet cake (two or three layers). What do you suggest in terms of doubling/tripling the recipe and size o...

I was planning to make three 9x13" cakes to make one rectangular three layered cake. I think if I double this recipe and divide the batter between the three pans, it should be just about right...?

The original recipe calls for baking in three round layer pans 8" diameter. Each can hold about 12 cups.
Sheet pan volune is about 25-30 cups.
So, make a double recipe & the layer might be a less deep than from the 8' pan.
Not clear from your question if you want to cut one sheet pan cake so it makes a 2-3 layer rectangular cake or bake 2-3 sheet pans and make a large layered rectangular cake.