Convert a 40 pin female 2.54mm pitch header to screw terminal blocks
You could make an adapter board which would have


male pins to mate with your existing 2x20 female
screw terminals of any style you like
mounting holes, which match the mounting holes on your motherboard.  This would make the construction more robust.
other components of your design


I haven't seen screw terminal with the right pitch to mate with (or replace) your female 2x20 connector.  I doubt that such screw terminal connector exists.