I've been thinking about this a little more.
Paul does say in the 1 Cor. 15 passage:
Not all flesh, is the same flesh (1Co 15:39 ROT)
I think this could be a key to the issue; if we are arguing whether the body is "flesh" maybe we are equivocating about two kinds of flesh.
42 Thus, also the resurrection of the dead: it is sown in corruption, it is raised in incorruption,
43 It is sown in dishonour, it is raised in glory, it is sown in weakness, it is raised in power,
44 It is sown a body of the soul, it is raised a body of the spirit; if there is a body of the soul, there is also of the spirit:--
What I think is significant here, is the pronoun "it" is all written as referring the same antecedent. "It is sown," what it? The body. "It is raised," what it? It can't be a new it at this point. And yet we are told clearly this new body is fundamentally different—yet still the result of resurrecting the old body. So, in a way, it's kind of a combination view; we could easily call the new body a spiritual body, and yet it was raised, clearly here anyway, from the old one.
45 Thus, also, it is written--The first man, Adam, became, a living soul, the last Adam, a life-giving spirit.
46 Howbeit, not first, is the [body] of the spirit, but that, of the soul,--afterwards, that of the spirit.
Due to the brackets here I think these particular verses contrast soul and spirit, rather than body and spirit.
47 The first man, is of the ground, earthy, the second man, is, of heaven:
48 As, the man of earth, such, also, the men of earth, and, as, the man of heaven, such, also, the men of heaven;
49 And, even as we have borne the image of the man of earth, let us also bear the image of the man of heaven.
Clearly here, the heavenly Jesus is distinctly referred to as a "man" even though he is "of heaven." There is a sense of continuity and progression here, as one form of man changes into another form of man.
50 And, this, I say, brethren,--that, flesh and blood, cannot inherit, God's kingdom. Neither doth, corruption, inherit, incorruption. (1Co 15:42-50 ROT)
It seems there could be a "flesh" that is not made of "corruption" perhaps.