Derech HaMelech, you wrote:
“We aren’t mevatel mitzvos for the sake of chillul Hashem. It’s not a chillul Hashem when the question is a mitzvah. If you have any source that says otherwise, please put it on the table.”
See Yevamos 79a: Dovid HaMelech executes Shaul’s descendants for what Shaul did to the Givonim. The Gemara asks that it is assur min hatorah to kill children for their father’s crimes. The Gemara answers that R’Yochanan said “mutav sh’t’aker os achas min hatorah v’al yischallel shem shomayim b’pharhesya.”
Further down the same amud the Gemara says that the bodies were strung up for a whole season. The Gemara asks that the posuk says that we cannot hang up a body overnight. The gemara answers that R’Yochanan said “mutav sh’t’aker os achas min hatorah v’yiskadesh shem shomayim b’pharhesya.”