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May I ask something of your expertise?...

The mass of the Sun 'attracts' the mass of our planet ... not directly, but by creating a field in which the motion of our planet is effected. Is that correct?

If that is a correct notion, the question then becomes, what about mass causes this 'field' influencing other masses? ... Don't physicists define the 'thing' causing the influence, creating the field, 'gravitons'? And if there are gravitons, doesn't it appear that these gravitons are actually influencing the spacetime of the universe (the background field in which masses exist), and that affected spacetime is that which then acts upon the other mass(es)?

Yes, I'm reviving the old 'ether' notion, in a way. But what I would like to address is the possibility that the field of spacetime is influenced by the space and time bound up in mass. I'm not so much addressing discrete physical quanta, as in 'particles' of gravity, as I'm trying to address the notion of 'dimensional quanta' (wound up dimensional phenomena) bound up in discrete physical phenomena you call sub-atomic particles.

The mass of the Sun 'attracts' the mass of our planet ... not directly, but by creating a field in which the motion of our planet is effected. Is that correct?

Perfectly.

If that is a correct notion, the question then becomes, what about mass causes this 'field' influencing other masses?

To be precise, it's energy that creates the gravitational field, not mass per se. In practice, mass is far and away the most significant concentration of energy in any physical system.

... Don't physicists define the 'thing' causing the influence, creating the field, 'gravitons'? And if there are gravitons, doesn't it appear that these gravitons are actually influencing the spacetime of the universe (the background field in which masses exist), and that affected spacetime is that which then acts upon the other mass(es)?

This is a tricky question to answer, because we don't know much about gravitons. We simply do not have a viable quantum theory of gravity. So I will confine my answer to General Relativity.

The gravitational field (per GR) is a curvature of spacetime. You are correct that the field is fixed with respect to the object (provided that the object does not undergo an acceleration). The field itself does not propagate, although changes in the field (caused by the acceleration of the object) do. Objects moving through the field will "see" the same field, because it is fixed with respect to the spacetime points through which the objects move (wholly unlike such subjective quantities as the angle of incidence for incoming photons, which gives rise to stellar aberration).

[Geek alert: Special Relativity dictates that the field seen by two observers with a relative velocity will be slightly different, but this is a subtle effect compared to what is being claimed by the "infinite speed of gravity" crowd. The Lorentz invariance is maintained because a compensating field (the "gravitomagnetic force") arises. This force is directly analogous to the magnetic force in electromagnetism. It arises for the same reason, but it has a much different form.]