But it is plausible for it to be hurtling 'upwards' at c (or 1000's x c)?
It was already explained to you that this is not even remotely the case. Read up on Special Relativity.
I have had grad level physics courses in relativity. If the earth is moving up as asserted at 32.17 ft/sec^2 you would reach c in 353 days. The earth is older.
So either you stop at c and lose gravity or exceed c.
You need to get educated on basic Newtonian mechanics
Hey, I took grad-level SR, too! Still my all-time favorite course.
But you're missing something here. In your own frame of reference, you absolutely can accelerate forever, and paradoxically, you'll never hit c. The faster you go, the more you experience time dilation, which you'd never notice. To you, your acceleration is continuing as normal, but to the outside observer, your acceleration is getting slower and slower the closer you get to c.
Think of it this way - You're in your car travelling at 50 mph. You can step on the gas and feel acceleration, right? But if a cosmic ray were to pass you in the other direction going 99.999999% c, to it, you're already going nearly the speed of light and it might say to you there's no way you can accelerate another 25 mph because you'd pass c. Obviously, that's ridiculous. You can accelerate regardless of how fast you seem to that cosmic ray, just as you can accelerate regardless of how fast you seem to any other point in the universe.
Likewise, the flat Earth could be under a constant acceleration forever without ever reaching c. C is a limit of how fast you can observe another frame of reference, not your own.
That said, the idea of universal acceleration utterly falls apart for a variety of other reasons. This just isn't one of the reasons.