First off there is no such thing as 20kV gloves, I assume you are refering to a class 2 glove that is tested at 20kV but rated for max use of 17kV. Thats OK since you were working on 13.8kV.
Second, the DOE inspector is right about the FR clothing requirement (if 70E is required to be followed on-site), several posts (I.E Ron)had the correct reason for this. Remember Arc flash boundaries apply even when the live parts are not exposed, shock boundaries (LAB, RAB, PAB) only apply when the live parts are exposed. (If you say there were no energized parts, then why the hotstick and gloves?)From the sounds of it this transformer has exposed live parts in the HV section (Lighting arrrestors)
Third, hot sticks are considered PPE per the 70E. They should be tested every 2 years if used as a primary means of shock protection, your gloves were your primary means of shock protection (If tested within the last 6 months) so you are OK on that one.
Basically, you are going to have a hard time defending you position, instead you may want to look at getting some(quality)70E training.
