I've been in that situation before, and usually they're going too fast to drag something like a carolina rig or drop shot out of the back of the boat. Any bottom contact bait, whether it's a ned rig or texas rig, is guaranteed to hang up and your boater isn't going to want to go back 100 feet to unsnag you. So you'll be doing nothing but breaking off and retying all day long.
A good solution I've found is a 3.8 Keitech Fat Impact swimbait on an exposed hook like a Strike King Squadron jighead. I personally like the Owner Flashy Swimmer because it's weedless, but expect that you're going to lose a few baits to snags, so a more inexpensive jighead may be the way to go.
Cast it out a good ways and run it as close to shore as you can. You'll be targeting fish hidden in the nooks and crannies that the boater may have missed. If the boat is going too fast for it to swim properly, give it some slack and let it glide for a second or two. Even click open the bail and let it go to the bottom before closing the bail and pulling it forward again. Sometimes there will be a fish on it when they hit it right as it dies.
Eventually as you work it, your bait will end up so far in back of the boat that you'll need to reel in and start over.
Use a longer rod, like 7'6" or so, to give you a good amount of slack to work the bait with. You'll also be fighting line stretch, so I highly recommend 20lb braid tied to a 2 or 3 foot fluorocarbon leader of 15 or 17 lbs. I wouldn't go less than 15lbs because when you do catch one, you'll be fighting the fish as well as the forward movement of the boat.
As for it being called trolling, if you're holding the rod and physically working the bait, you can credibly claim that you're working the shoreline exactly like the boater is doing at the front. And if that's all he's giving you to work with, then you really have no choice.