Please install latest nightly found below and see if your issue persists.
www.joomlapolis.com/downloads/doc_details/640-community-builder-nightly-build
I can't see a reason why conversiontype parameter would be endlessly looping nor can I confirm it here using dev build (same as latest nightly currently). Ensure all your CB plugins are also up to date according to our compatibility table below.
www.joomlapolis.com/cb-20-addon-status
If the issue persists even with latest nightly and up to date plugins begin disabling 3rd party plugins 1 by 1 to see if that resolves it as it's possible a CB plugin is modifying the configuration XML incorrectly.
If issue still persists please PM super administrator login credentials as well as FTP credentials and will debug further.
Some more digging shows that the 11th stacktrace entry (Countint from the top, libraries/CBLib/CBLib/AhaWow/View/RegistryEditView.php line 4684) will never complete (I think that the loop happens within the $this->_list_options it calls.
I have a breakpoint in the following line (4684, which is the return $this->selectList() )and it is never reached.
Here's an (highily uninformed, only spent ~20mins looking through) observation:
The 11th stacktrace line (the one mentioned before) calls
$this->_list_options( $name, $node, $control_name, $options, $node->children(), true, $value, $ignoreClass );
So the 10th stacktrace is _list_options() (same file) which for me reaches line 4646 which is:
$this->_list_options( $name, $node, $control_name, $options, $insideParamToRender->children(), $otgroups, $value, $ignoreClass, $index );
So it kinda loops back on itself.
Bear in mind that this 4646 line never finishes execution or it'd return back to the 11th stacktrace (it's the last line of the _list_options() function).
That's normal. You need to understand the XML structure for it to make sense as to what it's doing.
The first node is the <param node. The children nodes are <if nodes which call PHP to test if the image processing software is available (e.g. tests for ImageMagick, GD, and Gmagick). Inside of each <if node is a <left and <then node. The <left determines the left data to compare with (our PHP call) and the <then is the actual result if the <if becomes true. So in this case the <then has a <option child node, which is added to the select when the condition is met. Line 4646 is where it's sending the <then node back through _list_options to allow the child <option node to be output.
The only way I can see it getting stuck in this loop is if for whatever reason it can't find the <then, which I can't see that happening unless the XML structure was modified.
My best guess is you've ImageMagick and/or Gmagick installed, but not configured correctly or not meeting its requirements correctly. I believe it's recommended to also have Ghostscript if Gmagick is installed. Have you tried uninstalling ImageMagick and Gmagick entirely?