We present the second in a series of studies in which we have searched for undiscovered neutron stars in supernova remnants (SNRs). This paper deals with the six largest SNRs in our sample, too large for Chandra or XMM-Newton to cover in a single pointing. These SNRs are nearby, with typical distances of <1 kpc. We therefore used the ROSAT Bright Source Catalog and past observations in the literature to identify X-ray point sources in and near the SNRs. Out of 54 sources, we were immediately able to identify optical/IR counterparts to 41 from existing data. We obtained Chandra snapshot images of the remaining 13 sources. Of these, 10 were point sources with readily identified counterparts, two were extended, and one was not detected in the Chandra observation but is likely a flare star. One of the extended sources may be a pulsar wind nebula, but if so it is probably not associated with the nearby SNR. We are then left with no identified neutron stars in these six SNRs down to luminosity limits of ~1032 ergs s-1. These limits are generally less than the luminosities of typical neutron stars of the same ages, but are compatible with some lower luminosity sources such as the neutron stars in the SNRs CTA 1 and IC 443.