Location, Location, Location...Its hard to find big rainbows in a put and take fishery because most of the fish wont last long enough to grow to trophy sizes. Might try fishing Greer to Turner stretch with lures...There are more big fish up there because of the bait and size restrictions, or you can fish differently on the water you are currently fishing.
Buy some good polarized glasses and spend some time hunting for big fish instead of fishing your way down the river. Once you find the type of water they prefer, find similar areas on the river, and start refining your presentations so you can catch them..
Another hint..Fish at peak times and be there first or last.......Dawn, Dusk, peak moon phases.......Also, what kind of bait are you using? Sculpins, Minnows, Crawfish are the big bites that large trout prefer. Plus bigger baits keep the dinks off. Cheers.