Root Cause, if I read your picture, it looks like you have about 780 feet by 200 feet. If that’s correct that’s not to bad for a surveyor but still not cheap. I’d say gps is not going to work, the trees are too thick. I would use conventional equipment and run a random traverse along your boundaries. This is just done by using a total station and using landscape spikes for random points located near the boundary. You measure the angles and distances between them and also the property corners. Then go back and put points on line. It would take 6 to 10 points to do it.
Cost? Before I retired they were charging $150 an hour for my time. I figure it would take about 10 hours if you were helping me. This assumes your boundary corners are in. You can see depending on if it was quicker or longer than 10 hours it could cost $1000 to $2000 in a hurry. Some surveyors come cheaper, some cost more. When I was younger I didn’t like land owners helping me. As I got older, I learned they were good help for a couple of reasons. One, they know the property better than me and know how to get around on it. Two, they get to see how difficult it is, how the equipment is and why it’s expensive.