I'm not a lawyer, and I can't give legal advise, but the courts are there for you to ask to be compensated for the value of the lost trees. The documentation that you present will be all that the judge, jury, arbitor, insurance adjuster, etc. can use to determine the value of the lost trees. The neighbor will not be presenting any information about tree value, so you must assemble that data yourself.
One appraisal involved trees lost when an orchard ranch was logged off by one of the parties in a hostile divorce division of community property. Several methods were used to determine the value of the loss.
The loggers accidently started a brush fire when disposing of tree branches. The fire department log established the date, participant identities & location of the incident. The date was used to query the mills purchase records of the wood bought from the logger, establishing a baseline value of the claim.
The amenity tree value was arrived at by using the Basic Value formula developed by the Council of Tree & Landscape Appraisers. The irrigation system to the orchard was shut off during escrow, and the trees died in the summer heat, triggering lost Crop Value computations from previous years harvest income.
Keep in mind that the diminution of value in your land is actually a war of words. The only way a court can truely assess the market value is by a sale record showing how much the property sold for. The trees are merely improvements on that real estate.
Since comparing the sale price before and after tree loss is impossible, an estimate attempts to convince the judge how much the value would be if the property was sold with the trees still intact. Important values in your case can be determined by a real estate appraiser and a tree appraiser working in conjunction with an attorney.
If you value your trees, bet the cost of hiring these professionals against the risk of losing their fees if you lose in court. If you sue, expect to pay at least $15,000 in costs, which the court may elect to add to the dollar amount of the judgement in your favor.
If you collect for the value of the lost trees, the lawsuit overhead may still make you a loser if the judge decides to require each party in the lawsuit pay their own attorneys fees.