Maybe there is a built in way to do what you are looking for. However I solved it with a custom content modifier.
Create a snippet called 'fromContext' and add the following:
if( empty( $options ) ) { return $input; }
$context = $modx->getContext( $options );
return $context->getOption( trim( $name, '+' ) );
save the snippet.
(btw, the trim( $name, '+' ) is required because there seems to be an issue with removing the ++ from a system setting)
now you can just call your system setting like this:
[[++site_url:fromContext=`your-context-name`]]