Hi Matt,
I had not looked at this in a while because I really don't use it myself. But I just looked into it and figured out the problem. It must be when I introduced the configurable installation system I forgot to configure a needed setting for this module. Here are the steps to fix it on your intallation.
1. Using a text editor open the file Web/Setup/applications/mojoportal-core/FeatureDefinitions/90400_WebPartModule.config
2. Paste this in, replacing the current content.
<?xml version="1.0" encoding="utf-8" ?>
<featureDefinitions>
<featureDefinition
featureGuid="437a19b0-ef57-4963-b311-a1e13d9d883c"
supportedDatabases="MSSQL,MySQL,pgsql,SQLite,FirebirdSql"
resourceFile="Resource"
featureNameReasourceKey="WebPartFeatureName"
controlSource="Modules/WebPartModule.ascx"
sortOrder="500"
defaultCacheTime="360"
excludeFromFeatureList="false"
icon="blank.gif"
>
<featureSetting
resourceFile="Resource"
resourceKey="WebPartModuleWebPartSetting"
defaultValue=""
controlType="TextBox"
regexValidationExpression=""
/>
</featureDefinition>
</featureDefinitions>
3. Save the file, upload to server if needed
4. Visit SiteRoot/Setup/Default.aspx to make it reconfigure this feature.
Now when you click the gear next to the title of the WebPart moule you'll see the dropdown hopefully showing your web part.
Keep in mind that web parts that require settings don't really work in the content system because they don't have the webpart manager to manage their state. So to be usefull in the content system they need some useful default state. They work as expected in the MyPage feature but your mileage may vary in the content system depending on the web part.
Hope it helps,
Joe