Any reason the high side of the shed roof can’t intercept the existing garage roof further up the pitch? Then you could use open web trusses which although deeper are lighter and potentially cheaper than a wide flange. Attaching them higher also gives you more clear height with a longer span.
I dislike coins too, but mostly because a dollar is the smallest useful denomination and anything below is rounding. In a 1900 era world where you could buy something material for a nickel or dime, it was worthwhile to use those coins.