Recurstive query parent child speed
Well, with the help of Rick James' remark I managed to find the answer.
I installed MariaDB 10.2.5 (10.2.2 or higher required) and imported all MySQL data files by just copying the files in the Data dir to the MariaDB Data dir, and running mysql_update on the MariaDB database.

WITH RECURSIVE tree (parent_id) AS (
    SELECT parent_id FROM link_parent_child WHERE child_id = $ChildStartID$

    UNION ALL

    SELECT c.parent_id FROM link_parent_child lpc
    JOIN tree t ON t.parent_id = lpc.child_id
)
SELECT parent_id FROM tree


It really is that simpel :|

What are CTEs