...but I do think you've made a critical error in saying that JWs believe that Jesus followed the Law perfectly.
I studied with the JW's 40+ years ago and had to double check this morning before I replied to make sure that idea is still current thought. It's rampant in the writings of Franz in the 60's, but JW literature seems to avoid theological discussion of that caliber today.
I'll provide quotes below, showing it's still valid.
The counter-balance for Adam's sin was that Jesus, the second perfect man, did not sin. That's the JW doctrine, if not a general Christian doctrine. Keeping the Law could not atone for Adam's sin because Adam did not violate the Law (there being no Law at the time to violate).
Understood.
But what is the tangible proof that Jesus did not sin, if not for the fact that he kept the Law in every respect? (i.e. Perfectly) In Pauline theology, (Which is pretty different from what Jesus actually taught) the Law is the tool that exposes sin.
The JW publication, United In Worship of the Only True God states on page 147:
"Using the Jews as a sample of the imperfect human family, the Law exposed all the world, including each one of us, as sinners, liable to God for punishment. (Rom. 3:19, 20) Thus it emphasized the need for a savior for mankind, and it led faithful ones to Jesus Christ as that Savior. In what way? It identified him as the only one who kept the Law perfectly, thus the only human who was sinless."
This is what the JW Bible Encyclopedia, Insight On The Scriptures states:
"The Law was “holy,” “good,” “fine” (Ro 7:12, 16), and anyone who could fully live up to this perfect Law would prove himself a perfect man, worthy of life. (Le 18:5; Ro 10:5; Ga 3:12) For this very reason the Law brought condemnation, rather than life, not because the Law was not good but because of the imperfect, sinful nature of those under it. (Ro 7:13-16; Ga 3:10-12, 19-22) The perfect Law made their imperfection and sinfulness especially evident. (Ro 3:19, 20; Ga 3:19, 22) The Law in this respect also served to identify Jesus as the Messiah, for he alone was able to keep the Law in every respect, proving himself a perfect man.—Joh 8:46; 2Co 5:21; Heb 7:26." (Volume II, pp. 602-603)
So a JW who assents to the notion that Jesus broke the Sabbath really is punching big holes in their own Ransom doctrine. Even though they toss the words, "Atone" and "Atonement" around JW's actually subscribe to the theory of substitution when it comes to the Ransom. It's a subtle distinction, but it does directly relate to the quotes from JW literature above.