We consider some consequences of local conformal symmetry in spacetime in terms of new backgrounds for string and field propagation. These backgrounds which preserve this higher gauge symmetry generically include regions of spacetime where the effective gravitational constant becomes negative; these are separated from the usual regions by spacetime singularities. The higher gauge symmetry is a remnant of the Sp(2, R) phase space gauge symmetry studied in Two-Time physics and allows for relations between seemingly distinct Hamiltonian systems and displays their hidden symmetries. This modification to include patches of field space with "anti-gravity" leads to a dynamical tension for the bosonic fundamental string. We revisit the simplest non-trivial background, the SL(2; R)/R coset manifold or the 2D Lorentzian black hole and find that it allows a geodesic completion by looking at the point particle limit of the folded-string classical solutions. We also study some toy models for Hamiltonians with sign flipping terms and show that the free field theory is regular from the point of view of observers in the gravity region. Some general directions for studying field propagation in the extended spacetime are discussed in order to see if these methods provide a class of less singular classical backgrounds for interacting theories.