Fake owls/hawks etc won't do a thing. They soon suss out they are not for real. As for attracting crows, forget it. Crows are carrion eaters so don't bother the pigeons one iota. I should know because we have a small stream near us called Crowbrook, (simply because there are so many crows around here). The crows and pigeons eat together in the meadow next door.
Most effective thing would be a real hawk, such as a peregrine falcon or Harris hawk, which you release each day or two after proper training. Only problem is, if they catch a pigeon, or any other bird, they won't come home until they have devoured it and need to feed again which may take a day or two, (assuming they don't catch something else in the meantime).
Using fishing lines to try to stop birds going in trees is like trying to push water uphill. Where are birds supposed to live?Do you want the pigeons to get a mortgage?Years ago we had fishing lines stretched between tall trees with a flying plastic hawk silhouette suspended on a vertical line . There was a realistic floppy thin plastic cover fixed to it which flapped in the breeze as it swung about.
Its the only thing that really works but the downside was it got tangled quite a lot.
Edit: similar kind of thing,
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