Steps to reproduce the issue

When trying to implement custom fields into my extension I hit a road block when trying to do it in frontend editing. This happens if the context of the frontend edit (eg sermonspeaker.serieform) is different from backend (eg sermonspeaker.serie).
This is also the case for com_content (content.form vs content.article) but that case is handled by the fields plugin in its getParts method (https://github.com/joomla/joomla-cms/blob/staging/plugins/system/fields/fields.php#L600-L646) and thus it works.
It does two things:
1. First it has two hardcoded mappings:

$mapping = array(
    'com_users.registration' => 'com_users.user',
    'com_content.category'   => 'com_content.article',
);

That obviously needs to be removed as it will show that exact issue.

1. It tries to lookup the context from the database if the second part is "form":

if ($parts[1] == 'form')
{
    // The context is not from a known one, we need to do a lookup
    // @todo use the api here.
    $db    = JFactory::getDbo();
    $query = $db->getQuery(true)
        ->select('context')
        ->from('#__fields')
        ->where('context like ' . $db->quote($parts[0] . '.%'))
        ->group(array('context'));
    $db->setQuery($query);
    $tmp = $db->loadObjectList();
    if (count($tmp) == 1)
    {
        $parts = FieldsHelper::extract($tmp[0]->context);
        if (count($parts) < 2)
        {
            return null;
        }
    }
}

While it is nice to do some sort of fallback lookup, this shouldn't be tied to a specific name of the second part. In our case, this currently solves the issue for com_content but wouldn't help my component since I have multiple items and the query would return 3 contexts.

Expected result

Being able to save custom fields in frontend for 3rd party extensions

Actual result

Custom fields aren't saved for 3rd parties in frontend if the front- and backend contexts don't match.

Additional comments