Newton's God

The following three claims from the General Scholium of Newton's Principia have never made sense to me:
God "is not duration or space, but he endures and is present. He endures forever, and is everywhere present; and by existing always and everywhere, he constitutes duration and space. ... He is utterly void of all body and bodily figure."
What I cannot understand is how anything could exist always and everywhere, yet be neither body nor space nor time. Is there some further option for Newton? (Additionally, what does it mean that God 'constitutes' space and time?)

One of my students cleverly noted that Newton introduced the notion of a mutually attactive force between every two bodies in the universe; perhaps this can serve as an analogy for a Newton's God, giving me the 'further option' I'm hoping for -- since such a force is neither body nor space nor time? Unfortunately, in that same Scholium, we find an important disanalogy between the universal attractive force and God:
"In him are all things contained and moved, yet neither affects the other: God suffers nothing from the motion of bodies; bodies find no resistance from the omnipresence of God."
Presumably, any supposed force that affects nothing at all is not a force at all.

Are there any other possibilities for helping Newton out?

p.s. I found the following attempt to save Newton, from my old teacher Ted McGuire, in his "Existence, Actuality and Necessity: Newton on Space and Time," Annals of Science 1978 (how did people do research before the internets?):
"We can plausibly reconstruct the following argument. To say that God is everywhere with respect to space, is to say that one and the same individual exists at each place in extended space. To make such a claim is a contradiction only with respect to the manner in which extended things exist spatially. For they cannot as complete beings exist at once in each "part" of the place they occupy. But there is no contradiction in holding that an essentially non-extended being is capable of so existing. ... God is therefore omnipresent just in the sense that he remains numerically and unalterably the same individual at all places whatsoever. The conception appears paradoxical. However, Newton would claim that it only seems so, if we persist in imagining God's presence in space as we think of bodies individually occupying their determinate places." (p. 506)

But we can't allow ourselves the premise that Newton's God is "an essentially non-extended being," since in the General Scholium, Newton (apparently) says exactly the opposite. (Ted is right that Newton's God is incorporeal, but that isn't the same as non-extended -- think of Newton's absolute space.)