Use headsepline without reducing the text body height

In a document that uses the class scrreprt and the page style headings, how can a horizontal line under the header be introduced with class option headsepline=true without decreasing the text body height?

Consider the following image comparing headsepline=true and headsepline=false

As mentioned in the KOMA script documentation, the header is considered a part of the text body if headsepline=true. However, I would like to preserve the available height for text (due to a tight page limit I have to obey). With other words: how can I move the red line to the green line?

Use

\documentclass{scrreprt}


The headsepline option sets automatically headinclude=true. headinclude=false changes it back.

\documentclass{scrreprt}


\documentclass[headsepline,headinclude=false]{scrreprt}