The buoyancy of Dyneema would be equivalent to line with a density of 0.03 g/ml, so it would be equivalent to line with more or less the same strength, but weighing only 3% as much (unless Dyneema loses significant strength when wet).
Close. It would be equivalent to ~ -0.03 g/ml.
I wonder if any FEer would try to use this with the appropriate tension to keep it perfectly level and claim Earth is flat?
But that does also provide one key part:
If the region in the middle is lower than at the edges, then there is literally no way for a FE to explain it.
"Sag" in this case would be upwards.
It seems that at breaking point, over 1000 m, it would be higher by roughly 1.5 cm, while the curvature of Earth is roughly 2 cm.
That means it should still sag a big, but it would require 2.5 GPa.
Dropping it to 1 GPa would produce 3.7 cm upwards, meaning it would still go up.
So we need a heavier fibre.
Perhaps coat the fibre in something heavier than water to make it match water?