To clarify -- I do not have before and after experience with an LSx swap.
But, regarding the milage, I think you should uderstand that much of the difference you've heard about with LSx milage is a direct result of the fuel injection (which is for real) and the gears (which you could use with the old motor). In my wife's C5 Corvette, we get 27 to 30 MPG on the highway. But that's in Sixth gear, rolling along at about 70-75 MPH at only 1500-1600 RPM. The car is quite light, and certainly slippery. In the old (now gone) '69 Vette, we'd get 16 MPG, but were turning 3500 RPM at 70 MPH. Big difference. BTW -- The '69 also had more horsepower.
I'm not saying the engineering and engine management in the LSx motors doesn't have an impact, as I'm sure it does. But it's not the only reason for the extraordinary milage many of these cars produce.
Build a smooth running, mild street engine that produces torque all the way down to 1500 RPM, put a 0.50:1.00 ratio top gear in your transmission, and you can likely get north of 23 MPG too, on the highway with an old iron block 350 in your heavier Firebird.