Had the same experience several times. Can’t have crowing cockerels in from late winter - fall.My two 16 week cockerels have started having a crowing competitions. I don't mind it during the day, it's just the wee hours of the morning that it's unbearable.
It took me up to 3 months to rehome them. I made a few different adds to sell (and praise) them. Always managed to give the away for free /sell them for a very small fee (like $3).I'm looking for another option other than culling them. I've listed both on multiple sites for free rehoming and no takers (it's been a week).
I don’t know how your chances will be where you live.
A cover is not enough. A tiny bit of light and even noises from the neighbourhood can trigger cockerels to crow.Would covering the run do they can't see the sunrise stop the early morning crowing? I go let them out at 8am and my neighbors are usually off to work by then. If I could stop the pre-dawn/early morning crowing I might be able to keep them.
Some say it helps if you keep the cockerels out of sight and far away from the hens.
The best solution is to put the cockerels in a very dark shed or a special rooster box with a few pipes for fresh air.
And then there is a final possibility to get a few no-crow collars. Some people say its a torture for the rooster. Some have accidents with them. But its a possibility if nothing else works and you don’t want to cull.
Good luck!