  We study a variational class of generalised Ramsey protocols that include two
one-axis twisting (OAT) operations, one performed before the phase imprint and
the other after. In this framework, we optimise the axes of the signal imprint,
the OAT interactions, and the direction of the final projective measurement. We
distinguish between protocols that exhibit symmetric or antisymmetric
dependencies of the spin projection signal on the measured phase. Our results
show that the quantum Fisher information, which sets the limits on the
sensitivity achievable with a given uniaxially twisted input state, can be
saturated within our class of variational protocols for almost all initial
twist strengths. By incorporating numerous protocols previously documented in
the literature, our approach creates a unified framework for Ramsey echo
protocols with OAT states and measurements.
