I have lots of forsythia to so I know what you mean. I have not personally moved one .In the spring when it as finished blooming I trim tops and stick them in the ground they take root easily. Sorry I could not have been more help on moving it.

There's probably lots of plant material that would provide spring color and year-round screening - Which ones are best suited for your consideration will depend on many factors: some weather guidelines (where you live, or what USDA zone), what exposure (N, S, E, W?) and amount of sun, the type of soil and drainage in this location, and the amount of space you have (both width and height).

As for moving the forsythia, my experience has been that they don't resent being moved. We've moved several about the yard, some as large as 6' high. Our soil is very poor and sandy, so I prepare a large new hole generously amended with well-composted shredded leaves and a touch of cow manure. We take as large a root ball as we can manage, but usually still wind up cutting a few extremely long roots. We then set the plant at the same height at which it had been growing, water in well, add leaf mulch on top, and make sure it has sufficient water until we feel it has settled in. The leaves may look a little limp at first, but they perk up before long. I find they bloom well even the first spring after the move, which I usually do in late summer/early fall. Now, maybe we've just been lucky, or have a particularly hardy type of forsythia, so I hope someone else may chime in here and that you will consider carefully before you move the plant. I knew full well there was a risk I could lose each one, but was willing to take that chance.