OK - first off - DON'T LISTEN TO LES!
What
@bnw is saying about markers is IMO what you should look for and probably should have at minimum before cutting down the trees. If you have paved streets and sidewalks, there should also be what appears to be a nail head or a plastic hub (about 3/4 to 1" round, usually yellow), or a mark on the street side of the curb for those sides. Being that you have a corner lot, if you can find them, you should be able to easily figure out the back corner if you have your lot description. If you don't, your county assessor most likely does.
If you can't find any of that, what bnw said about a piece of rebar is true but it can even be a wood stake pounded into the ground if it was done on the cheap.
If you are a landscape architect, ask some of your colleagues or maybe your local trade organization. I'm sure they have some recommendations on surveyors that won't cost you an arm and a leg. Someone might do it as a professional courtesy hoping to get future work from you. That's how I had mine done when I was a landscape supervisor.
I think there is little chance of getting anything back from what you spent on tree removal unless they were a hazard and you have something from him saying he'd like them gone as well. If you have been using the land for more than 7 years, you could possibly have an adverse possession case - especially if no one objected to you cutting down the trees and you can show you paid for it and that there is still evidence of where the trees once stood.
Bottom line though is that now you are in protection mode. Like it or not, you really do need to establish your property line. If his fence is on your property and you do nothing to prove it, he can use adverse possession on YOU and it generally (from my understanding) takes less time if you have allowed him to build a fence on it. If it proves that his fence is on his property, you will need to protect your other line or face losing it when you or your neighbor sells his house.
I hate to be my dad but any time you do anything near a property line that can be considered permanent, you need to have a survey or already know the exact location of your property lines.
Before you get a survey however, you should explore all the other options to see if you can find existing markers. They should be there in some form. Call the city and see if someone can tell you what kind of markers they accepted or are commonly used in your area. Sometimes, your home's paperwork will even say things like "from the property hub at the NW corner....".
Good luck.