Cheef, some will say this is counterproductive. If fishing a water with a big head of carp but it's not a commercial styled match type fishery and going on your signature; "hates commercial fisheries;" it won't be?!!
On waters like Linear I've found by fishing with your lines taut and up in the water spooks the carp out of your swim but has no ill-effect on tench present. Basically fish a lead/feeder tight lined to your reel.
Another alternative is to find an area where you know tench feed, bait it up with hemp, maggots and/or casters, wait until you see positive signs of tench in the swim; rolling and/or bubbles, and then fish it.
Dawn and dusk fish to showing fish, again rolling and fizzing. Either with a feeder or better still a small spod and a lead. If you're not talking of large shoals of tench, more pods of 2-5 fish, fish a float or lead baited with a bunch of red worms.
If the fish are close enough feed loose offerings via a catapult.
Or stalk the margins.
The list of possibilities is endless, really for a more thorough answer, more details on the fishery are needed; size, depth, type of lake, fish stocks (both size and numbers).