I would go with the 6wt. IMO goldeye aren't the greatest fighters despite how much they jump, however, there is always the chance that you could tie into a pike in which case its nice to have the extra backbone.
I fished the NSR twice this past weekend. First evening I fished for about 45 minutes and ended up getting 5 goldeye and 1 25" pike that followed me in to about 3' of shore before it decided to hit. Second evening I was out for about an hour but was only able to manage 2 goldeye. Either way, good fishing considering I can just walk from my door to the river.