I didn’t check your algebra, but those curves looks right to me. The increasing difference at the (high) dan end means that the EGF system expects higher winrates when (high) dan players play somewhat weaker opponents to reach/maintain a (high) dan rating. That expectation coincides with historic data from EGF tournament games (with mostly longer time settings).
Perhaps the OGS curve fits better for the faster time settings that OGS players tend to use, or perhaps there just isn’t much historic data in OGS about established/vetted high dan player performance against near-peers, so data above rank 30-35 can’t be fitted well.
Either way, I don’t think it matters if log or exp is used. It’s the overall shape that matters, and the shapes are quite similar, at least in the kyu range.