Safe generation of $k$ points on a curve such that the mutual discrete logs are hard?
It would be more confidence-inspiring to choose a hash-to-curve method and pass consecutive integers through that.  There is a current (2019-05-16) internet-draft surveying hash-to-curve techniques with references, draft-irtf-cfrg-hash-to-curve.  The most popular method for Ed25519 is Elligator 2.  Since invertibility is not required for your application, you could also just use the hash-and-pray technique: for each $i$, find the smallest $j$ such that $H(i) + j$ is an $x$ coordinate on the curve, where $H(x)$ is (say) $\operatorname{SHAKE128-512}(x) \bmod{2^{255} - 19}$.