Does anyone have any tips or ideas for finding large mouths in rivers that have very little, if anything, in the way of backwaters. I plan on fishing my local tournaments on the Rock River this year and I have no problem catching limits of smallmouth, but I'm not sure what to do if I want to go largemouth hunting to up my weight. I've seen good largies out of the river, but don't really know how to target them.

One thing that is important in all bass fishing and should definitely not be overlooked in river fishing is to look for any sort of cover or structure, this can be crucial in a tournament. Also, if the river bends at one point, the inside of that bend will normally hold fish because of the current seam, I know this tactic is often used in trout and salmon fishing, so give it a shot in practice and see if it pays off.

I don't get to do much river fishing for bass...but when I do...a productive technique is drop-shoting bridge pilings.

Unlike smallies the largemouth prefers to wait in quiet water right next to current. They don't hug boulders out in the current. They set up to ambush whatever comes down along the bank. Unlike most lakes, most of the bass will be looking upstream. They will feed heavily until spawning. Find a break along the bank, maybe a tiny eddy pool caused by a jammed log, or the tip of a rock jetty, etc. Cast so that a lure swims with current to the bass, then maybe let the current bow your line to let it swim in a wide arc back to the boat. An ideal setup for me is to find a good eddy pool that sucks the lure into the pool so I can swim the lure out passing a bass, for a reaction strike. There are lots of techniques to try. Fish every spot that is "different" from typical bank. Risk hangups working the toughest spots you can find, where many anglers pass to avoid losing baits.
Hope you do well.

As Ouachita said small mouth bass love current large mouth bass don't , look for log jams , wing dams, fingers ,points, island weeds, down trees, any thing that creates slack water.   A deadly tactic for fishing a down tree or log jam is to position the boat up current then cast out  a floating crank bait and let the lure drift into position right next to a tree or log jam then twitch it and be ready cause you need to take control if one hits .

And flip any cover. Flip deep in heavy cover.