If you can rule out that the space will ever be converted to habitable, then you can undersize a tad from the tabulated values. As Tony mentioned above, its normally the deflection limits that dictate the size rather than the shear or bending limits. (i.e the floor would be likely to damage decorative finishes, feel to bouncy, and upset inhabitants of rooms below, long before the timber is in danger of actually failing)
For your application (i.e. with the new beams some distance above the existing ceiling, and not ceiling to be mounted on the underside of the new joists), deflection beyond normal limits is a non issue. So it reduces to a problem of what is adequate in terms of bending and shear loading on the timber (assuming you don't mind it feeling a little more bouncy than "normal" given that you know it is still structurally sound).
Perhaps a play Tony's excellent bit of software might be in order (assuming there is still a demo version available for download?)