I think I finally solved it. Turned out I did need to care about outgoing traffic.
As soon as I added a static route for the LTE connection to go through the GRE tunnel, I started working. So I added a mangle for incoming packets and marking connection if the from-sub1 mark has been set.
This post helped my a lot: http://forum.mikrotik.com/t/pbr-ensure-traffic-leaves-the-same-interface-it-arrives-on/75060/1
Will test a bit more later today, but it is looking good.