Doublespacing is moving my page number

Question

I'm using the KOMA-Script report scrreprt to typeset my PhD thesis and the graduate school requires that the main text be double spaced and that the page number be in the top right. When I enable double spacing the page number moves down a little bit. How can I solve this?

Here is a MWE that reproduces the problem:

\documentclass[12pt, letterpaper]{scrreprt}

\usepackage{setspace}

\usepackage{scrpage2}
\pagestyle{scrheadings}
%this code clears the header/footer
\clearscrheadfoot
%then puts the page number in the top right
\rohead[\pagemark]{\pagemark}

\begin{document}
\chapter{ch1}
hello
\chapter{ch2}
\doublespacing
hello
\end{document} 

Answer 1

Adding \setstretch{1} to the header seems to help:

\makeatletter
\g@addto@macro\headfont{\setstretch{1}}
\makeatother