[ben_w]

A mass with negative effect on local curvature, would I think still follow the same geodesics (i.e. fall down).

Same in Newton, though there it would be GMm/r^2 = F = ma but both m have the same sign so acceleration is the same regardless of value (including -ve), though if M was negative then both +ve and -ve valued m would accelerate away rather than towards.

Conservation of momentum and energy is conserved because they're mv and 1/2mv^2, so an isolated equal and opposite +- pair co-accelerating has a total of zero of both all times.