Questions for Amillennialism

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His kingship is therefore incarnational (not spiritual), even though the location of that reign is presently heavenly rather than earthly.

That statement forces a false dichotomy by misdefining "spiritual". And it causes your argument to fail. And it separates what Scripture consistently joins.

The incarnation is profoundly spiritual because the definition of spiritual regarding the incarnation is "of/by the Spirit". The incarnation is explicitly the work of the Spirit (Luke 1:35) "Spiritual" in the context of amil and the current reign of Christ from heaven does not mean "non-bodily". And a person cannot successfully or even reasonably redefine the meaning of a term to mean something other than the way the one using it, is defining it.

Scripture itself does not divide "incarnational" = bodily, human and "spiritual as being non-bodily or Spirit only.
The Son becomes incarnate by the Spirit
The son ministers in the power of the Spirit
The Son is raised by the Spirit
The Son reigns and gives the Spirit

You are trying to protect the idea that Christ's kingship must be exercised through his human nature as the sole operative category. The problem with that is it isolates Christ's humanity from the Spirit's role and also from his divine nature.

And 1 Cor 15:44 breaks your argument. "It is sown a natural body; it is raised a spiritual body.? A body. Yet called spiritual. "Spiritual" does not mean "non-bodily". It means Spirit-empowered, Spirit-governed.

 

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If Christ truly reigns “in a glorified physical state,” then his reign must be exercised through that glorified physical humanity, which necessarily entails a visible, embodied, localized, historical kingship. To affirm the humanity while denying its operative is not consistency but a contradiction.

Patience my friend. That happens at the end of this age when he returns. Don't rush him. He has lambs to gather into his kingdom. He has a means of doing so, like any good king has means of obtaining his purposes. Jesus send his earthly armies, the saints out into all the world with the gospel so his sheep might hear his voice and follow him, he sent the apostles to lay the doctrinal foundation of his church, and men to canonize it, wisdom to translators and those who designed the printing press. He sent men to reform his church when the evil one made a mockery of it in the Roman church. He continues to do this work through men. He is gathering his flock, and he will continue to gather his flock until the last one is brought in. No one gets to tell him how the King does this or when.

And since he remains the Christ with two natures, human and divine, and always will, then all these things are done by his human and divine natures. In sending the Spirit to regenerate his people he is not crowning the Spirit king nor is the Spirit taking kingship for himself. To claim that is not only unorthodox it is illogical.