OP you have my sympathies. We have 3 massive oak trees which cast a lot of shade in our garden, and over the years we've lived here they've grown many feet taller. One in particular has NEVER been trimmed, in the 30 years we've lived here. Our gardens are fairly small so it puts 2 gardens into complete shade for most of the day.
We have tried over the years to politely persuade the 3 different owners to get the trees cut back, in each case offering money towards it. One was polite and pkeasant, but explained that she loves the tree so she only has dead wood removed. Another owner was totally unco-operative, refused to discuss it and is a bloody minded sort who has dug his heels in about the tree, despite polite approaches from several neighbours. It is far too big and quite lop sided, so may eventually fall down. Not wishing harm to people but if it fell on his property it would cause massive damage and I would not have any sympathy for him.
The third owner she'd like hers pollarded, but did not have any money to contribute towards it. We bit the bullet and paid for the whole cost of a fairly radical pollard job, so that has given us a bit more light. In your position I would try approaching the owners of the other trees and offer money towards the cost of a tree surgeon, and perhaps be prepared to pay all the costs yourself, as often people have an attitude of "well, it's not bothering me, but if you want to get it trimmed go ahead, if you are willing to pay".
The whole issue of huge trees in small gardens is a real bug bear with me, as the shadow can be severe enough to restrict what you can grow, and can make a garden very depressing. People can be utterly selfish about it, thinking that their right to grow what they want trumps other people's rights to do the same. I really wish the law would change, but sadly the high hedge legislation does not apply to single trees, no matter how massive they are. I admire large beautiful trees in parks, but they are totally inappropriate in small gardens.