IR keyboard codes mystery

As interpreted by the decoder. It is very likely that the keyboard uses a proprietary protocol, but certain codes manage to fool the decoder into recognizing the wrong protocol.

The logic analyzer is the best place to start. I would start the analysis by comparing signals for series of keys, like "a", "b", "c" or "1", "2", "3", looking at bit pattern changes, to see if there is a relation with the ASCII code. The code might also be column & row.

is the inconsistency for successive presses of the same key

Separate "press" and "release" encodings like an ordinary wired keyboard?