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I am sorry to hear about this situation. On this website, I do not always get to give good news, and this is one of these times.
This is actually a very textbook case. In California, the Court gives them the right to seek reasonable cost of cutting back vegetation that crosses unto their property:
"It seems to be settled law that overhanging branches are a nuisance, and it must follow that invading roots are. The person intruded on by branches may cut them off; it must be true that one may cut off invading roots; it must be true that he who is injured by encroaching roots from his neighbor's tree can recover damages sustained from them. The right of action seems clear." Crance v. Hems, 17 Cal. App. 2d 450 - Cal: Court of Appeal, 4th Appellate Dist. 1936 (internal citations omitted).
Although not very ethical, it is quite legal for them to refuse to agree to the landscaping project (if it their choice whether to agree or not to) unless someone in your situation reimburses them for the damage your tree has caused on their property.
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