In your location ,it is perfectly OK on the Northside of property ,if you got full sun there.
You can move it right now,but you have to do the moving in the Evening,just before night come ,and( very important),you have to provide shade for about one week,using a patio umbrella.
Of course when you dig it out,try to ,get the roots intact,and if possible some soil left on them,and,fill the new planting hole with water prior of ,placing the tree in it.
Take the umbrella off,just before a rain starts,and the sky is cloudy.

"... We are going to trim the limbs that encroach on our property from the large trees."

I wish you luck. My neighbor talked about cutting a tree down for nearly a year. I offered to pay half the costs or to help him with it myself.

I finally gave up and cut down many of the enroaching branches that were touching and overhanging the roof of my house and which constantly drop pine needles and cones onto my roof and into my gutters.

He came back from work as I was finishing up and blew his top. We had a short hollaring match after which he called the local sheriff's office.

They sent a deputy out who took pictures and basically told him that anything hanging over the property line on my side of hisfence was mine and I was free to do with it as I pleased.

That was a year ago. We are speaking now, but it ain't like it used to be.

I wish you a better experience than I had.

I vote move it. Do what Herman said, he knows alot about figs.

Dave, sorry to here about your neighbor. Way to go though. If it is over your property then it is your property. My experience with neighbors is that most are less than ambitious. My neighbors on each side fall into this category. At least the ones across the street keep a nice yard, so when I look out the front window the view is nice.

I have the same problem the neighbor trees and my own shade trees puts shade on my figs I figured they are getting full sun from 6 AM to 10 AM and again from 3 Pm to 8 PM that is about 9 hours. I asked the neighbor to trim his trees but he does not do any thing to these trees. I hired a tree professional and he trimmed two of my trees to the bone and asked the neighbor permission and trimmed all his branches encroaching on my yard. After 1,000 cost my shade problem improved may be 25% but I am enjoying a lot of good mulch. From my reading 8-10 hours of sun is enough for a fig tree to survive.