I've had a CAM870 with the same issue out of the box, but unlike yours only with the trigger assembly fitted. I'll share my solution in case it brings you any help.
I had to gently file down the angle shown below on the rear of the cradle arm that engages with the trigger assembly. I had to round it very slightly on the outer edge to get it to release smoothly when each shell was loaded and the arm was in its furthermost front position as it was just catching and preventing it from resetting properly.
For completeness here is the opposite mating part linked to the action bar lock that slides over that angle in the cradle arm (I lightly filed the upper edge but it likely didn't need it):
Can you freely move that part with the assembly out, or is there friction? With the hammer locked back (safety on to protect your fingers!) you should be able to freely move it with only light sprung resistance and the action bar lock should more smoothly. The carrier 'leg' on this side was very slightly misaligned on one of mine (it was twisted slightly). I've taken the trigger out of one to look at it and if the carrier is twisted inwards at the bottom it can touch the action bar lock and cause it to jam when the hammer is locked back (it should release again when the cradle arm moves forward). I can also see some light wear where the trigger connector touches the body of the trigger assembly so it might benefit from some grease along that face of the body. If that were to catch it would also prevent the trigger resetting properly, but on mine there is too much free movement for it to stay caught as it is not under tension.
To test it out if you pull the trigger to release the hammer but the action bar lock is not allowed to return properly then the next trigger pull will not disengage the hammer. The trigger will also have no resistance to the pull. It's hard to capture on camera but if it looks like the top picture after locking the hammer back then it has not reset properly so look for the cause of the friction. It should look like the bottom picture:
You say "only when I hold the trigger in and press the action bar lock a bit, it fires" and I can reproduce that by preventing the trigger connector from fully resetting.
If you have not already read them, you might find the following two threads on a different forum useful: http://airsoftcanada.com/showthread.php?t=162618&page=3 http://airsoftcanada.com/showpost.php?p=1911329&postcount=3
On the second link near the bottom N_Force shows some adjustments you can make to the trigger set that may help you. I see he has applied grease to the face I mentioned above, possibly to help prevent this problem.
Also, APS made a video for removing and reinstalling the trigger assembly which if you've not done it before may be helpful.
https://www.youtube.com/watch?v=FJiRtURPPy4
