The thing is, if you read Einstein carefully, he never says that gravity is produced by warping space. Never; not a single time. It's a common misunderstanding of his theory, but it's not a part of relativity at all.
What Einstein said is that gravity is an effect of warped spacetime, and he also agreed with you that space itself is not a physical thing that could be warped or compressed.
So if spacetime is just a combination of time and space, and the space itself cannot be warped, then that only leaves the time element. That is the thing that is actually being warped to produce the effect we see as gravity. Gravity is an effect of warped time, not warped space.
Now, since time is just something we use to measure rates of change it might seem just as nonsensical to talk about warping time as it does to talk about warping space. But essentially what it comes down to is that things change at different rates depending on the density of matter and energy in their vicinity. Now why that is happening is the real question!
“he also agreed with you that space itself is not a physical thing that could be warped or compressed.”
No he didn’t.
Relativity gives me a headache.
You can only measure velocity relative to some other object, not relative to empty space itself, and you cannot move faster than the speed of light relative to any other object. So if you launch two spacecraft, each going 90% of the speed of light relative to you but in opposite directions, how fast are they going relative to each other?
I know there is a mathematical formula to calculate it (which is far beyond my recollection of my 40 year old college calculus and physics classes), but conceptually it makes my head hurt.
“So if spacetime is just a combination of time and space, and the space itself cannot be warped, then that only leaves the time element. That is the thing that is actually being warped to produce the effect we see as gravity. Gravity is an effect of warped time, not warped space.”
This is absolutely false. The three dimensions of length are altered by gravity just as surely as the fourth dimension of time; in special and general relativity, the only difference between length and time is their opposite signs in the distance metric.