There is an issue with the semantics here. "Flat" has two relevant definitions here. Something being "flat" can mean that it is 2 dimensional in reference to a 3 dimensional construct - if so, that's a perfectly acceptable reason to think of something as "higher dimensional". Something being "flat" can also just mean that it's incredibly thin (i.e.: "flattened out"), which obviously doesn't mean anything "not flat" is higher dimensional.
The reason I bring this up is because of the paper example provided here; yes, we're not higher dimensional to paper, but that's because paper is just incredibly thin, not 2 dimensional. Paper still has a third dimension to it, it's just small. Paper fits the latter definition, not the former. In the case of the fabric of existence, the former definition is relevant, not the latter. So this example about paper doesn't mean anything to the discussion on the fabric of existence - this is just an issue with equivocation. This is obviously a bit of a tangent from the point of the thread, but I've seen several people pointing out this example so far without giving it due skepticism, hence why I felt it was important to bring this up.
As for the main crux of the thread (that being whether the time stream/fabric of existence is qualitatively superior to the space beyond), I'm unfortunately currently just neutral, with a leaning towards disagreement. My knowledge of this aspect of the verse is primarily based on what scans and statements I've examined as a part of my involvement with these threads, and I've not seen anything particularly decisive so far. To elaborate more - I believe there is clearly some relevant meaning to things like how Professor Paradox states that the realm of the Time Stream is "Beyond the Space Beyond", and I'm not convinced that we can simply rationalise these statements away. At the same time, though, I don't think anything presented thus far is definitive enough to make such specific claims about qualitative superiority. I will be keeping a close eye on this thread (and potentially giving input where it may be relevant) in the hope of reaching a more decisive conclusion, but as of now, I have little in terms of a clear opinion.