I'm not sure exactly what the problem is here, unless you have limited
yard space on your property. Don't these trees add value to both
properties in terms of privacy and scenery? More than half the tree
will be on his side. And your neighbor paid for them.

If you do have limited space, then this is a problem, as leyland
cypress can grow to 60'+ and 15' across. In this case, there are
other screening trees that would have been better choices.

As for mowing issues, no matter where you plant them, unless they are
way inside his yard, you still can only get so close to them on your
side with a riding mower, leaving an uncut area.

If you really must do something, then I would try explaining to your
neighbor that you have the right to trim the trees where they extend
over the property line. Explain that with them two feet from the line
if they are trimed they will likely die because there would be
relatively little left of half the tree. Plus they will look like
hell on your side, but soundsl like he may not care about that. If
that doesn't work, then as a last resort, maybe a letter from your
lawyer explaing the above.