You are correct it does look like an NEC signal, based on the images. The last bit is the repeat part.
It also looks like your IR reveiver may be an issue.....what is the model # (link) for the IR receiver.
You should not be getting anywhere near nSecs with a standard IR receiver.
....OH I just noticed that you are using an IR LED. The output will not be 100% digital which is what the LA is expecting.
That may explain some of your issues.
You could try the following, using an IR LED: Poor maker’s Infrared receiver
..if you don't have access to an IR Receiver.