Way over thinking this in my opinion. If as you say in a later post the lead leaves a crater in the silt then being inquisitive creatures the Carp would be more than likely to investigate it than be wary of it.
Chod rig all the way for me on that kind of lake. 4 or 5 oz lead so it plugs in the silt deep to set the hook firm.
I used to fish a lake that, at one end where the gravel workings used to be the sandy/silt (more like sludge) was upto 3feet deep in places (I know this as I was stuck in it once in my chest waders, quite frightening if I'm honest). Plenty of anglers fished the area for little reward. You would see the big plumes of coloured water when the fish were there. My first time in there and I used Chod rigs on 6foot of lead core, 4oz leads on and caught half a dozen. 4oz lead in silt becomes a pound of lead or more, sets the hook, job done.