Yeh, it's the auto sear as you've just confirmed. When you push it forwards, it sits in the position it would for semi (i.e. disengaged), so that's why it works again. Usually the bolt would smack that sear forward like you are there, so that could be a culprit too.
Either it's damage to the surface of the hammer (not likely as I can kind of see it there) or it's misaligned - as you say - or just very worn. We kind of need to look at the bottom of the auto sear though as that's where it contacts the hammer. Finally, it's also possible some dirt has built up in your selector and is pushing the sear further than it should be.
So it could be a case of disassemble, clean and reassemble those two parts or - at worst - a new auto sear (just under £10). It's up to you if you want to try it yourself or get someone else to do it. I will say there are plenty of reassembly guides out there for the selector or and auto sear, but if you've not the time then it may be best to send it to some place like Milspec Solutions (though be ready to pay a fair amount of money).
I can't find anything on the compatibility of WA-compatible auto sears with LM4 designs. I'd say they should work, and at most may require a small bit of filing - this could be come a problem if you send it to a professional as not many will keep the OEM parts as specific as this in stock (indeed, I couldn't find anywhere selling an original sear other than the KWA website).
If it were me I'd remove the sear and check it for damage. At worst I'd have to replace it later (a little fiddly) and at best I can know where the problem is and then maybe sort out a replacement part myself rather then sending it to someone who's just going to tell you that they need to order the part in and that it's going to take weeks for that to happen. I'll see if I can find anything on WA parts compatibility (because if they work then that's a lot of effort saved). Without that sear the only effect you'll get is that obviously you'll be locked to semi only.
Basically: It's either the bolt not pushing that sear forwards when you shoot or the sear is worn or misaligned.
Edit
Could you take a picture of the underside of your bolt too?