I read through the thread and didn't pick up on why you are using the isolation transformer. It should generally be unnecessary, unless something in the signal chain has a malfunction.
I would trouble shoot in the following order: Confirm your XLR cables are good and properly wired (use a multi-meter or cable tester), try the isolation transformer on another amp, try another isolation transformer on your amp, try a different mic pre. It appears you have done most but not all of these steps.
Beyond that, I don't find the GK DI to be particularly good sounding to begin with. Perhaps you would be better off using a quality DI.
I use it live to proactively avoid ground loops and damage from phantom power. I realize most amps have built-in phantom power protection measures, but I have read about some 1001RBs having issues related to phantom (though this could have been an older revision of the amp that was affected since they've been around for decades; mine was purchased new last year).
I do also have a passive Radial ProDI I could patch in after my pedal board, and I do have a Tone Hammer DI on my pedal board. That said, I have been using the Tone Hammer as an overdrive pedal with the GK so it's only on for a few songs. I like that the "woofer high cut" is passed through to the GK's DI in post-EQ mode as I am a tweeter-less flatwound user, and I like the independent level control.
I would expect a 1:1 (aka isolation) to measure the same on both sides.
You may have an impedance matching transformer rather than an isolation.
Can you post a pic or give any info (model # and such) that is printed on the device?
It's a Radial IC-1 Ice Cube. [Invalid or Expired Link Removed]