Md65536,
"I don't have a firm handle on curvature but I think curvature due to mass approaches 0 (flat) as distance approaches infinity, but it is still non-zero at any arbitrary distance???"
Yeah, that sounds right to me according to the warped space model, that matter warps the space surrounding it and is the cause of gravity.
" ... there is an intrinsic limit to distance based on time (concerning gravity). A mass cannot have any effect on anything outside its light cone."
(parenthesis added)
This is also valid but indirectly there is a gravitational effect of everything on everything else. The idea is that although it is outside your light cone now, for instance, it does and did effect its neighbors, which effected its neighbors, and so on, all the way back to you. If something is outside your light cone but could somehow disappear, then according to GR it could never effect you because its effects could not travel faster than the speed of light.
"That spacetime warps (consistent with SR and GR) is a fact of reality that I accept."
The warping of space (space-time) is unrelated to SR which says nothing about this. It is strictly a GR proposal. But of course the concept does not violate SR.
"...I don't think that all these beliefs are mutually consistent, and I'm missing some understanding of the meaning or implications of curvature..."
As to the meaning of flat space: it is what we see in the everyday world. It's the way other animals see the world. It is simply a three dimensional structure of reality which is the natural way that it appears to be to the unaided eye. It was the reality of physics up until Einstein proposed it differently. Remember, there is no evidence of any kind that I know of, that space is curved.
There is evidential support that gravity works in a non-linear fashion, not strictly according to the inverse square law of Newton. As to curved space: In Riemann geometry which is the geometry of GR, two parallel lines can eventually cross. There is no forth dimension involved (other than time) so that it is a type of non-linear geometry which Riemann said did not apply to the natural world, yet Einstein found an application of it in the equations of GR, whether right or wrong. If space is entirely flat at the largest scales of the universe, then at least the warped space/ curved space idea of Einstein is wrong. All observations so far seem to indicate that at least the observable universe appears to be flat.