Source?
1) The source for the halacha above is the Gemara Sanhedrin 47a. The Gemara learns it out from the depraved Jews who were killed in the time of the churban. They were clearly mechalel Shem shamayim barabim. See also Radak Yirmiyah 5:1
2) The source that מיתה is מכפר for chilul Hashem according to the mechilta is the passuk by the sons of עלי הכהן. They were מחלל שם שמים ברבים.
3) The numerous seforim who discuss the level of חילול השם and מיתה מכפרת are never mechalek. See for example ראשית חכמה פרק גידול בנים אות כח where he makes no distinction between the two.
4) If you still need a מקור בפירוש see the מרפה לשון (he was the one who appointed Rav Chaim Volohzhiner to be Rav of Volozhin) in עמוד התורה (p. 93 in the new edition) where he spells it out clearly.
I think it’s time to move on and close the subject.