You imply that you are not interested in the bream, but you don't say what you intend to fish for. A bit more info would be useful before anyone can help you.
I do hope you are not poaching on my estate.
Hmm, let me think, its an estate lake with a large head of bream and the question is placed on the carp board, errrrm, maybe Arctic char, no, its vendace........... Perhaps......
BJH, if its bream avoidance that's the priority, I'd start with bait. My usual way of avoiding bream is either of these two; tiger nuts over a bed of hemp, also you can swop the tiger nuts with maize but don't feed much maize as it'll just attract the snotty ones.
Or
The big boilie approach, 20mm or bigger. How you approach this technique depends on the head of carp in the water.
Anything from a couple kilos spread over an area of 20x20ft, down to a few crushed and whole boilies each cast with PVA.
Regards rigs, I'd go with a combi-link hook length using strip braid but also strip back the loop you attach to your swivel (link to mainline) as, if your lead gets embedded in the silt, your hook length can still hinge and lay flat on the deck. A 2oz square lead on a running rig will also help reduce the the lead getting stuck in the silt, so will clipping off, as you can effectively lower the lead/rig on to the water.
I'd use PVA to help reduce tangles and include your lead in it, again to lessen the chances of getting lost in the silt.
Another option which I'm shocked no one has mentioned. Stalk the margins, putting a handful of bait in likely looking spots and only fish for visible carp or definite signs of activity; clouds of silt from feeding carp, bubbles, carp rolling etc
And whatever you do, with the exception of when stalking,
DO NOT FEED FISHMEAL BASED PELLETS or crumb groundbait!