I think we're on the same page. I prefer the natural, mortal body vs supernatural/spiritual body. But it sounds like you're saying the same thing. Physical/natural/mortal body does not of course equate to "flesh" = sinful (which would have Paul supporting Gnostic dualism). And spiritual body doesn't mean a disembodied spirit/soul (for the same reason, and also because that's Platonic, not Judaic belief).
But the word "spiritual" does throw people because "spiritual" means something quite different today then it did then. In fact, if I recall correctly, "spiritual" is a wholly Christian concept that originated with Paul, the apostles, etc, and that means something along the lines of, "of the [Holy] Spirit." Hence, all the metaphors of sowing to the flesh vs the Spirit. And being born of the Spirit.
But because this is easily confused, I like the clarifying "natural" vs "supernatural" body to avoid thinking the resurrection body is a nonphysical disembodied spirit "body," which would make no sense in either Jewish or pagan thought.
Resurrection always meant physical, bodily resurrection, but like Jesus's resurrection body it is not a resuscitation of the mortal, decaying body back to life (like Lazarus, who still died later on), but a supernaturally transformed incorruptible body that will never see decay.
The Pharisees, of course, believed the resurrection wouldn't happen until the end times Judgment Day by God at the end of the world, and that this would be a 'national' resurrection of all the true, non apostate remnant Israelites.
But the idea of resurrection of a single individual was beyond comprehension in 2nd Temple Judaism. That is what makes Jesus's resurrection so radical. It's not simply coming back to life. 1 Corinthians 15 is teaching that the end-time Judgment Day resurrection that won't happen until the end of the world has already started in the person of Jesus Christ and the rest of us will soon follow suit. This is the inaugurated now-but-not-yet eschatology we see in the NT. The end of the world Judgment Day resurrection has already started---it started with Jesus. Jesus's resurrection signals the beginning-of-the-end! Pretty heavy thought!