The quasi-one-dimensional (1D) Ising ferromagnet CoNb2O6 has recently been tuned via applied transverse magnetic fields through a continuous quantum phase transition from spontaneous magnetic order to quantum paramagnet and dramatic changes were observed in the spin dynamics, characteristic of weakly-perturbed 1D Ising quantum criticality. We report here extensive singlecrystal inelastic neutron scattering measurements of the magnetic excitations throughout the threedimensional (3D) Brillouin zone in the quantum paramagnetic phase just above the critical field to characterize the effects of the finite interchain couplings. In this phase we observe that excitations have a sharp, resolution limited lineshape at low energies and over most of the dispersion bandwidth, as expected for spin-flip quasiparticles. We map the full bandwidth along the strongly-dispersive chain direction and resolve clear modulations of the dispersions in the plane normal to the chains, characteristic of frustrated interchain couplings in an antiferromagnetic isosceles triangular lattice. The dispersions can be well parameterized using a linear spin-wave model that includes interchain couplings and further neighbor exchanges. The observed dispersion bandwidth along the chain direction is smaller than is predicted by a linear spin-wave model using exchange values determined at zero field and this effect is attributed to quantum renormalization of the dispersion beyond the spin-wave approximation in fields slightly above the critical field, where quantum fluctuations are still significant.