i would forget about pulling fuses for now...there is a problem with the battery itself at the moment.
11.7v after being left disconnected overnight is a flat battery...slightly lower, maybe 0.5v, and the car wouldnt have started..its actually taken a 5 mile run to get the battery to read above 12v, and at 12.06v is still very low charge
imagine the battery was connected overnight, soon as it drops below 12v, then its quite plausible the alarm will mistake this for a voltage drop, such as a door being opened, it may or may not have triggered the alarm, but it may increase the drain as it tries to deal with the info...not saying this is whats happening, but its one of a number of possibles
the battery will also struggle to maintain a charge at that voltage with a normal amp drainage.
first step has to be, charging the battery to an acceptable level...get it to at least 12.3v after charging and left for couple of hours.
from there, i would personally leave it disconnected overnight before taking another reading..any drop in voltage more than 0.2v i would suspect a battery fault..even 0.2 is pushing it, ideally you will want to see less than 0.1v difference
if battery has sustained an acceptable voltage, then you can carry out the drain test and get a truer reading...11.7-12.06v is way too low