Get menu link siblings
So, I ended up figuring out some code that would let me do this, by creating a custom block and, in the build method, outputting the menu with transformers added to it. This is the link I used to figure out how to get the menu in the block and add transformers to it: http://alexrayu.com/blog/drupal-8-display-submenu-block. My build() ended up looking like this:

$menu_tree = \Drupal::menuTree();
$menu_name = 'main';

// Build the typical default set of menu tree parameters.
$parameters = $menu_tree-&gt;getCurrentRouteMenuTreeParameters($menu_name);

// Load the tree based on this set of parameters.
$tree = $menu_tree-&gt;load($menu_name, $parameters);

// Transform the tree using the manipulators you want.
$manipulators = array(
  // Only show links that are accessible for the current user.
  array('callable' =&gt; 'menu.default_tree_manipulators:checkAccess'),
  // Use the default sorting of menu links.
  array('callable' =&gt; 'menu.default_tree_manipulators:generateIndexAndSort'),
  // Remove all links outside of siblings and active trail
  array('callable' =&gt; 'intranet.menu_transformers:removeInactiveTrail'),
);
$tree = $menu_tree-&gt;transform($tree, $manipulators);

// Finally, build a renderable array from the transformed tree.
$menu = $menu_tree-&gt;build($tree);

return array(
  '#markup' =&gt; \Drupal::service('renderer')-&gt;render($menu),
  '#cache' =&gt; array(
    'contexts' =&gt; array('url.path'),
  ),
);


The transformer is a service, so I added an intranet.services.yml to my intranet module, pointing to the class that I ended up defining. The class had three methods: removeInactiveTrail(), which called getCurrentParent() to get the parent of the page the user was currently on, and stripChildren(), which stripped the menu down to only the children of the current menu item and its siblings (ie: removed all submenus that weren't in the active trail).

This is what that looked like:

/**
 * Removes all link trails that are not siblings to the active trail.
 *
 * For a menu such as:
 * Parent 1
 *  - Child 1
 *  -- Child 2
 *  -- Child 3
 *  -- Child 4
 *  - Child 5
 * Parent 2
 *  - Child 6
 * with current page being Child 3, Parent 2, Child 6, and Child 5 would be
 * removed.
 *
 * @param \Drupal\Core\Menu\MenuLinkTreeElement[] $tree
 *   The menu link tree to manipulate.
 *
 * @return \Drupal\Core\Menu\MenuLinkTreeElement[]
 *   The manipulated menu link tree.
 */
public function removeInactiveTrail(array $tree) {
  // Get the current item's parent ID
  $current_item_parent = IntranetMenuTransformers::getCurrentParent($tree);

  // Tree becomes the current item parent's children if the current item
  // parent is not empty. Otherwise, it's already the "parent's" children
  // since they are all top level links.
  if (!empty($current_item_parent)) {
    $tree = $current_item_parent-&gt;subtree;
  }

  // Strip children from everything but the current item, and strip children
  // from the current item's children.
  $tree = IntranetMenuTransformers::stripChildren($tree);

  // Return the tree.
  return $tree;
}

/**
 * Get the parent of the current active menu link, or return NULL if the
 * current active menu link is a top-level link.
 *
 * @param \Drupal\Core\Menu\MenuLinkTreeElement[] $tree
 *   The tree to pull the parent link out of.
 * @param \Drupal\Core\Menu\MenuLinkTreeElement|null $prev_parent
 *   The previous parent's parent, or NULL if no previous parent exists.
 * @param \Drupal\Core\Menu\MenuLinkTreeElement|null $parent
 *   The parent of the current active link, or NULL if not parent exists.
 *
 * @return \Drupal\Core\Menu\MenuLinkTreeElement|null
 *   The parent of the current active menu link, or NULL if no parent exists.
 */
private function getCurrentParent($tree, $prev_parent = NULL, $parent = NULL) {
  // Get active item
  foreach ($tree as $leaf) {
    if ($leaf-&gt;inActiveTrail) {
      $active_item = $leaf;
      break;
    }
  }

  // If the active item is set and has children
  if (!empty($active_item) &amp;&amp; !empty($active_item-&gt;subtree)) {
    // run getCurrentParent with the parent ID as the $active_item ID.
    return IntranetMenuTransformers::getCurrentParent($active_item-&gt;subtree, $parent, $active_item);
  }

  // If the active item is not set, we know there was no active item on this
  // level therefore the active item parent is the previous level's parent
  if (empty($active_item)) {
    return $prev_parent;
  }

  // Otherwise, the current active item has no children to check, so it is
  // the bottommost and its parent is the correct parent.
  return $parent;
}


/**
 * Remove the children from all MenuLinkTreeElements that aren't active. If
 * it is active, remove its children's children.
 *
 * @param \Drupal\Core\Menu\MenuLinkTreeElement[] $tree
 *   The menu links to strip children from non-active leafs.
 *
 * @return \Drupal\Core\Menu\MenuLinkTreeElement[]
 *   A menu tree with no children of non-active leafs.
 */
private function stripChildren($tree) {
  // For each item in the tree, if the item isn't active, strip its children
  // and return the tree.
  foreach ($tree as &amp;$leaf) {
    // Check if active and if has children
    if ($leaf-&gt;inActiveTrail &amp;&amp; !empty($leaf-&gt;subtree)) {
      // Then recurse on the children.
      $leaf-&gt;subtree = IntranetMenuTransformers::stripChildren($leaf-&gt;subtree);
    }
    // Otherwise, if not the active menu
    elseif (!$leaf-&gt;inActiveTrail) {
      // Otherwise, it's not active, so we don't want to display any children
      // so strip them.
      $leaf-&gt;subtree = array();
    }
  }

  return $tree;
}


Is this the best way to do it? Probably not. But it at least provides a starting place for people who need to do something similar.