I do not think ANY bike, with the exception of a motor bike, will up your speed 3 mph over 40k.

Maybe if you were on a single speed beach cruiser. Or a sit up tricycle, or maybe a full blown mtb.

But not coming from a vintage touring bike to even a Slice. Not going to happen without training.
Not in the long haul. You will be excited about the new bike, and your speed will get a small amount faster, but after a while, it wears off.
It's still you that is pedaling.