You've got me really interested and I really have to think about it before I answer...
I think that their timescape and your timescape may be compatible.
Time rotated therefore shorter in the direction of Radial Time: Dilation = slowed
Exactly. If you project your time vectors onto the vertical axis of a global, cosmological time, you'll get shorter projection of tilted vectors that are perpendicular to the slopes. In your case the shorter the projection, the slower the time flows. That would also mean, that your vertical time vector at the bottom of the valley should be shorter.
Sorry for repeating your statement with my own words. Why wouldn't it solve the problem with their timescape?
So what explains Dark Energy?
Me

Aaahh, now I get the main problem with their timescape (besides the first one you mentioned). They explain the expansion with these time flow differences. You're rigth, they're wrong about this explanation, but also not wrong about the timescape,
but you seem to be even more right about it because of your perpendicular time vectors. However, their cosmological time is also radial in your sense.
What's even more important to me, is that your vectors are not a measure of time which has passed since the BB, but only the measure of the
current time dilation at their points. I'm totally convinced, that
Now is everywhere and that spacetime temporality lies only in time dilaton (at each spacetime point) , that corresponds to g00 component of the metric tensor. I'm convinced, that time does not accumulate physically, but it's a very handful mathematical tool.
There is a Miss, who thinks very much your way in terms of the radial time, that is a radius of the expanding hypersphere, but she's a total freak. Don't even try to read her About Me, I warn you.
Knowledge is not power
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Now that I think of it, she actually thinks like both of us in part. You can relatively safely read her about me on Astronomy SE - it's light version.
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