Hey again,
As _modernnomad_ already mentioned, the root cause of my rejection was that the LMIA used in my EE profile was both expired, and not linked to my current (open) work permit. I'm not allowed to post links yet, but there is a page on the CIC website (Express Entry: Creating an Express Entry profile and requirements for entering the pool) which states "Express Entry candidates who are employed in Canada on a temporary resident work permit that was issued based on a positive LMIA do not need to acquire a new LMIA to support their expression of interest, even if the assessment expiry date posted on their LMIA has passed, should they meet the requirements below.". I obviously didn't read it carefully enough at the time, because if I had I would have seen that one of the requirements is that the candidate (me) be on a work permit tied to the same employer as the LMIA. Sadly mine is not. I am on an open (LMIA-exempt) work permit issued through the IEC (International Experience Canada) program.
The full story of that is that back when my first work permit (which was also issued under IEC) was due to expire, I reapplied for a second, whilst my company simultaneously requested an LMIA. We decided to pursue both options since time was an issue and the IEC could supposedly get me a permit much faster. That turned out to be true, I got the IEC permit and we let the (positive) LMIA go to waste.
Obviously it turned out to be a mistake to try and use that LMIA on my PR application (although I feel like most people would agree, looking at it from a purely human perspective, that my case for 'arranged employment' is about as solid as they come, e.g. over 2 years with the same company, including an admittedly expired and unused LMIA, and a continued offer following PR. It really seems like they were just being sticklers for the rules and refused me on a technicality).
But oh well, like I said, not worth dwelling on it. We literally submitted the paperwork for a new LMIA for me this morning so things are already looking up. I'll get that within a couple of months, get a new ITA, and hopefully have PR by next summer.