As a quick'n'dirty hack I made a skin copy with an extra closing div (that closes the unclosed div for me).

This fixes my issue but is really a hack. I'd be very interested if someone came up with a better solution.

Nope.  I tried it (pulling the title and solpart skinobjects out of the container contentpane) but the same thing happens.

In essence this (with all other html stripped out): 

<div id="dnn_AnotherPane" class="anotherpane">
<div id="dnn_ctr370_ContentPane" class="simpledimpleccontent" align="left">
<div id="dnn_ctr370_ModuleContent">
</div><!-- previous div ends simple container -->
</div><!-- anotherpane closes with previous div -->

...and the closing div's come from my container and my skin.  Was worth a try though.