If the higher-ups were trying to cover it up, why would they order extra tests? Especially if they knew it would reveal something suspicious?They dudn't order extra tests. The tests we know about were performed privately by Ivanov through his contacts. He was on dangerous ground here having been ordered to stop investigating and create a coverup.
This doesn't seem to agree with the case files. See vol 1 p. 370: https://dyatlovpass.com/case-files-370?rbid=17743
Ivanov appeared to have ordered the radiological testing via official channels on May 18. It is also clear from that document that Ivanov already knew, as of that date, that at least some of the four hikers' clothing had radioisotope contamination. The examination he ordered seemed to be mandated by criminal procedure, which would seem like common sense. If law enforcement detects radioactive contamination, then it shouldn't be ignored; of course professionals should be brought in.
The big question is how Ivanov knew that there was contamination in the first place.