scrbook open=left and =right for chapter and parts, respectively

Hi,

I am using scrbook to create a sort of two-sided catalogue that has parts and chapters.

Many of the chapters occupy only two pages and it would be useful to see both of them at once.²

1. Therefore I would like chapters in the main matter after the first part-page to start on the left
2. However, title page, table of contents, and part pages I want to start as usual on right pages.

If I use option open=left¹, all chapters start left (not only those after the first page-part, violating 1st and 2nd gets violated anyway.

If I use \KOMAoptions{open=left}¹ after the first part page, title, toc and first part page are ok, however after the first part page there are two empty pages before the first chapter, following chapters are OK, but following parts end up on the left:(

Enclosing each \part¹ with \KOMAoptions{open=right}¹ and afterward \KOMAoptions{open=left}¹ would get me a bit closer to a solution, but requires lots of fiddling. and I would end with empty double pages.

Any advise would be appreciated!
best
sven

MWE:³

\documentclass[10pt,twoside%
%,open=left%with this even the titlepage gets on a left page
]{scrbook}
 
\usepackage{lipsum}
 
 
\begin{document}
\frontmatter
\title{test}
\author{test}
\maketitle
\mainmatter
 
\part{Should start on the right}
\KOMAoptions{open=left}
 
\chapter{Should start left}
\lipsum[1-4]
 
\chapter{Should start left}
\lipsum[1-5]
 
 
\part{Should start on the right}
 
 
\chapter{Should start left}
\lipsum[1-5]
 
\chapter{Should start left}
\lipsum[1-5]
 
\end{document}

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