While I cannot promise I can walk that line perfectly, I have worked professionally with Catholics on translation and other theological projects. There is a very healthy dialogue between the two religions at present, part of which deals with a new understanding in Catholicism, namely that Catholics no longer believe in Superssionism and that the Jews are thus still in an active covenant relationship with G-d.
I cannot, of course, speak of the effects that this change is having on Catholic theology or practice, but I can use what I've learned through the years about Christianity and New Testament history to give some help in uncovering the problems JW theology has put upon itself by its peculiar reading of the Scriptures.
The idea that Christianity can exist without believing in a literal crucifixion or denying that Jesus was believed to be the very incarnation of YHWH is highly problematic. If these things weren't true, then there would be, for one thing, a very noticeable gap in Judaism's refusal to accept Jesus as the Messiah.
Witnesses tend to forget that as long as there has been a Christianity there has also been Jews claiming they don't believe in Jesus due to belief in his divinity and use and worship of the cross by Christians. Belief in Jesus requires what Jews see as defying the Shema, our most sacred prayer: "Hear, O Israel: Adonai is G-d. Adonai is One!" And the way the cross is used and displayed—well for Jews that's just plain idolatry.
If what the JWs claim is true, then how did Jews develop these counter-arguments regarding Jesus? If Jesus is just "a god" like the angels, why would Jews claim belief in Jesus violates the Shema? If Jesus did not die on a cross, why would Jews have arguments against its use in worship?
Until just recently with the release of the NRSV: Jewish Annotated New Testament (which is fruit of the Catholic-Jewish dialogue began in the 1960s), Jews had no access to or attempted to read the New Testament. Where did they get these ideas about the Incarnation and a cross and crucifixion (that is, not to mention our own history of the Second Temple era where we ourselves testify to the fact that Romans had a habit of nailing Jews to crosses who, by the way, weren't Jesus)? These Jewish counter-arguments are older than the Christian canon.
Jehovah's Witnesses do not think three-dimensionally. You can't take away "cross," the belief in the Incarnation, and you even have a problem with Petrine authority in the first century Church (as well as numerous other problems) if you take Witness theology as accurate. It doesn't work, and that's speaking for anyone whether you're a Jew or not.