Lifting the battery wire and measuring the post on the isolator will give you a false reading. To prove this, put the positive lead of your voltmeter in one hand and touch the post on the isolator. Of course have the voltmeter negative lead grounded. You will read full voltage if you hold the probes tight.
Take the wires off the isolator after taking a picture of them. Now bolt them together. Start it up and recheck. I bet things are working then.
The 27 volts is NOT getting a load from the batteries. You may have an external voltage regulator and due to a bad isolator it is not seeing that voltage feedback.
If this seems to clear things up then just change the isolator and see if all is well.
Always fix the "obvious" component failure first and don't try to understand or diagnose all of the symptoms.
If you had a loose/intermittent connection you could get all of the symptoms fo a bad alternator twice. Even the best technicians on their best days can easily miss something like that.