get dupe of this mechanism, put it on the top.
the rotation will not matter as a jointed pring or pivoted ball (like wiper motor, or getto jail tatoo gun) will do the trick.
so now when the mech rotates it will pull or push the door from the top.
if you use a spring from the back you will get the benefit of more leveraged distance.
short spring and a lever to release it, this will give the long movement from the spring in a short space,
think switch blade but slower...good luck tuning it tho.
i dont see why the mech as is needs to go tho