Once your PPD is positive, it may remain positive. So repeat skin testing should NOT be done. Instead a chest x-ray is done to monitor for active tuberculosis (TB).
With a positive PPD and negative chest x-ray there is a 10% chance that you will develop active disease in your lifetime. This is why preventive treatment is advised, like INH. Since you could not tolerate the complete course of INH, rifampin for 4 months might be considered. It is important that you seek medical care immediately if any symptoms of TB develop, such as cough, coughing up blood, decreased appetite, weight loss, fever, night sweats.
You should NOT have another PPD. It will still be positive. I am in the same situation. I documented everything. I have copies of my positive PPD, as I changed employers a couple of years after I converted. I had the requisite chest xray and then I went to an infectious disease doc and took INH for six months. I had blood work to check for liver enzymes.
Enlist the help of an infectious disease doctor if your employer insists on this idiocy. These are nonmedical people trying to deal with a medical issue. They will only listen to a physician. If you do not have documentation, you must trace backwards to get it.
The ID doc would be the person I would ask regarding the abbreviated INH course. You may need a chest xray but I am just speculating. After my positive PPD I had a chest xray and it was negative. If it had been positive I'm sure I would have been on either double or triple drug therapy. This happened to a lab friend who had a questionable spot on her chest xray after PPD conversion. She was on three anti-TB drugs and couldn't tolerate them. They cut her back to two of them and she was on them for six months, I believe. You do not want to create a situation where you have partially treated TB, as this leads to drug resistant strains. The fact that you were only on INH leads me to believe your chest xray was negative.
If you work at a hospital, you may also be able to make an informal visit to one of the pathologists there and tell them of your plight. They may be able to cut through some red tape for you, or connect you with the ID doc that deals with microbiology. My PPD was so painful and swollen I absolutely do NOT want to go through that experience again. I had 18 mm induration and my whole forearm swelled besides.
Good luck.