Jim,
As always, good thoughts and questions.
"Mr. Chesterton, in all fairness to your students, Paul's words on the subject (especially 1 Corinthians 15) aren't perfectly clear."
I realize Paul isn't perfectly clear. The historical Christian tradition, however, is. Out of the three basic Creeds of Christendom (Nicene, Apostles, Athanasian), two explictly mention "the resurrection of the body" and the third (Nicene) looks "forward to the resurrection of the dead." In context, this means dead. At the least, 2/3 explicitly mention the resurrection of the body. That's not conclusive, but it provides grounds to pause when no one in the class has any sort of understanding of that doctrine. But, I recognize this was a throwaway defense of my students (who I love).
As for your other (more substantial and interesting) criticisms, the most interesting is this:
"Paul seems to want to have it both ways--the resurrection is "real," but not "physical" in the normal sense."
The clause might give the criticism away--what is the "normal sense" of physical? If the resurrection happened, then this "normal sense" might not obtain. To quote Lewis (in the same essay), "It is the present life which is the diminuation, the symbol, the etiolated, the (as it were) "vegetarian" substitute. If flesh and blood cannot inherit the Kingdom, that is not because they are too solid, too gross, too distinct, too "illustrious with being." They are too flimsy, too transitory, too phantasmal."
Incidentaly, this explanation (that "physical" is not as substantial as we think it) would also explain Jesus's ability to walk through walls on this earth. It's like walking through a mirage.
"I'm curious as to how the distinction between material and spiritual is defined in any coherent sense."
It seems as though the distinction between "emotion" and "nerves" is pretty coherent and if property dualism is plausible, it seems a short jump to substance dualism. After all, if my thoughts are distinct from my neurons, what is doing the thinking? How is that not coherent? Or is that not the distinction you were thinking of?
"I'm also curious as to why it "matters" (to use a horrible pun) whether the resurrected body is a material body, rather than a spiritual body."
I'm curious as to what a "spiritual body" would be. I agree that there are spiritual substances, but "body" seems to be a term that is limited to matter.
Lest you think I am incoherent, I will offer an explanation of Paul's use "spiritual body." The genitive here can be a bit confusing. I think it implausible (given the nature of the argument and for other reasons) that Paul means by the term "body of spirit" or "non-physical body." Rather, the "spiritual body" seems akin to the "spiritual man" of 1 Corinthians 2, the "man who lives through the Spirit." Given all of Romans 8 and Paul's use of "spiritual" in 1 Corinthians (as well as his statements about the body being a "temple" of the Spirit, the most natural meaning of "spiritual body" in 1 Corinthians 15 is "a body that is under control of the Spirit."
This leads to your final question:
"I'm also curious as to why it "matters" (to use a horrible pun) whether the resurrected body is a material body, rather than a spiritual body. What difference does that "Gnosticizing" make to the average believer?"
I am tempted to list specific ways I think it makes a significant difference, but will refrain (unless asked). Athanasius's "soteriological axiom" was, "That which was not assumed was not redeemed." Christ took on the whole of man (body and soul) to redeem and transform him. If a Christian does not recognize that basic truth, I would suggest they have not yet learned to offer "their whole selves", body and soul, to God. Do this: read Romans (in the NASB) and circle every time Paul mentions "body." If you do, then 12:1 (perhaps the most quoted verse on sanctification) makes a lot more sense; "I urge you...to present your bodies...to God....which is your spiritual service of worship." Present the bodies, have the minds renewed. The Christian spiritual life cannot stand on only one of these two pillars.