Binary neutron star mergers can be sources of gravitational waves coincident with electromagnetic counterpart emission across the spectrum. To solidify their role as multimessenger sources, we present fully 3D, general relativistic, magnetohydrodynamic simulations of highly spinning binary neutrons stars initially on quasicircular orbits that merge and undergo delayed collapse to a black hole. The binaries consist of two identical stars modeled as Γ=2 polytropes with spin χNS=0.36 aligned along the direction of the total orbital angular momentum L. Each star is initially threaded by a dynamical unimportant interior dipole magnetic field. The field is extended into the exterior where a nearly force-free magnetosphere resembles that of a pulsar. The magnetic dipole moment μ is either aligned or perpendicular to L and has the same initial magnitude for each orientation. For comparison, we also impose symmetry across the orbital plane in one case where μ in both stars is aligned along L. We find that the lifetime of the transient hypermassive neutron star remnant, the jet launching time, and the ejecta (which can give rise to a detectable kilonova) are very sensitive to the magnetic field orientation. By contrast, the physical properties of the black hole+disk remnant, such as the mass and spin of the black hole, the accretion rate, and the electromagnetic (Poynting) luminosity, are roughly independent of the initial magnetic field orientation. In addition, we find imposing symmetry across the orbital plane does not play a significant role in the final outcome of the mergers. Our results suggest that, as in the black hole-neutron star merger scenario, an incipient jet emerges only when the seed magnetic field has a sufficiently large-scale poloidal component aligned to the initial orbital angular momentum. The lifetime [Δt≳140(MNS/1.625  M⊙)  ms] and Poynting luminosities [LEM≃1052  erg/s] of the jet, when it forms, are consistent with typical short gamma-ray bursts, as well as with the Blandford-Znajek mechanism for launching jets.