I'll admit I wandered down this particular rabbit hole when the BA II first came out, I got one for my Ric 4001 because..... Geddy. I chickened out and never installed it on the Ric. It's still on my Warmouth Frankenjazz, and works perfectly surface mounted with no recess, and it's a fretless, so it's plenty low. Is the neck geometry different enough on an Aerodyne that the bridge needs recessing? My nephew has an American Aerodyne, the bridge is not recessed. I wonder if the "recess" on the OP's bass is just a big dent in that butter-soft basswood when they torqued the bridge down in the factory? At any rate, I'll agree changing bridges makes little to no difference tome wise, but can be a big improvement functionally or aesthetically. I suspect Leo knew the bent saddle looked like the cheap thing it was, hence the chrome bridge cover.