I just had time to try another test just using the Norman LH2 heads that I keep on my copy stand most of the time.
Adjusting the strobe power from 50 to 100 to 200 W-s, there was no significant difference in color temperature from one setting to the next--at most 10 degrees K, which is within the range of variation from flash to flash on a single setting. This is as it should be, since in theory the flash output is regulated by changing only the duration.
On the copy stand I use the heads with 5" reflectors that have an opal glass diffuser and a very uncalibrated white handkerchief over each head, and the color temperature is 5480-90K--almost exactly what it should be. If I remove the reflectors, the temperature of the flashtube is a little on the blue side 5950K--enough for the IIIF to recommend an 81A.