Here's an idea.
A lot of commercial fisheries have several pools. How about dropping your local ones a line and asking them whether they have a fishery on site that has a good head of tench but few if any carp.
If they don't know there is a demand, they can hardly be expected to cater for anglers looking to avoid the pond pigs.
Afterall, from their perspective, carp make sense. They cost less than half the price of tench to stock, they grow faster, they are more robust and lots of people never shut up about how much they like to catch them.
Been there, and done that Ken, with private owners, club committee/members, and as you know, those that cast a bait in these places. The reply is usually, 'this is what the punters want'. The equation is, more fish in pond = more bums on bank = more revenue for 'fishery'. Carp being the usual cheapest option, with a few alien/exotic species thrown in for good measure. I prefer being regarded as an angler, not a 'punter' or customer, but it's now a business, and that's how we are seen, with the catching of fish being the 'product' on sale.
There was a time when I had to actively search for a water that held a few carp, now it's harder to find one that doesn't, and that includes many of our rivers.
Angling is more than just catching fish, if it wasn't it would just be called 'catching'......... John