Cybercrone...I may be able to help you...or at least make you cry! (just kidding) I think I am the root queen! We bought this house and there were 3 trees
in the back yard...BUT the root system was exactly as yours and even some that were above ground. So, we called the tree
man and here is what I know.
There is a "hard plate" below the ground that keeps the roots from going down...they grow upwards to find water..there is pretty much nothing you can do for the hard plate short of dozing the yard up completely and putting some gravel or some kind of drainage system in which is pretty darn expensive even for a small yard.
We had 2 of the trees
taken out (we desperately needed the room) and then they came in with a grinder and ground up almost the entire yard trying to grind the roots. The tree
we left in is a maple, and we are seriously considering taking it out and having the rest of the yard ground up. The roots from the trees
are tearing our privacy fence up badly. Even with them grinding the yard...we STILL find mega roots when tilling or trying to put in a new garden bed. I cannot tell you how close to the tree
you can do this without killing it. We even have problems with the neighbors elephant ears roots growing
under the fence and all the way to the middle of our yard! It is just an ongoing problem that we have to deal with constantly. I cannot tell you for certain that you have the hard plate thing going on...but it sure sounds like it to me. If you have a tree
service in your area, they will probably caome and give you an estimate or tell you what is going on without a charge...It would be worth checking out. You can rent the grinders from an equiptment rental place...but here it was almost as much to rent the machine as it was to just have some one come and do it. Maybe this will help give you some ideas as to where to start.