batteries can be fickle sometimes... I really stress on scrubbed connections every time I mention them..
I bought a new one this year for the C14, again, as I didn't pull it out during the winter, nor did I attach my Tender to it... it had like 3V this spring, and even charging, and cycling it, on a manual charger (no auto shutoff, so I had to keep an eye on it during the cycling), I still didn't trust it... it would bump up to 12.8v-13.2v, and then drop down overnight to 12.7v...
then, when I did a "bleedoff" using a headlight 'high beam" bulb for 1 minute ( I do this to get a reference point, as a 60watt load like that, puts a 5 amp drain), it would drop to 12v...
so, I replaced it and installed a new one, which I activated, and charged prior to install...
surprisingly it only went up to 13.0v also, and bled down to 12.8v... but it's new, and it works... strangely, the old batt which I cycled a dozen or so times, and actually bounced around on the bench between charge cycles, restored itself, and continues to hold 12.7v, and when "load tested" was remarkably still good... go figure... I spent $$ on a new one, and should have trusted the old one, but now I have a spare, and it's inside on the tender, warm, and waiting.... and this winter, like in a week or so, I'll pull the new one out, and "parallel charge" both on the tender all winter..
the immobilizer error thing does make me ask, have you ever taken the FOB battery out, and started the bike using the passive chip only? If you have replaced a FOB, and this is what you have, and it was 'programmed', they may not have programmed the 'passive chip', and BOTH need to be done with a new FOB, as it's a 2 step operation for programming.... just curious.
report back, sounds like you have it all in hand tho.