I have about the same setup, for my peas and tomatoes. I planted mine at the very outside edge of the bed (about 8" away from fence). They all are doing very well.

Are they in a bed or planted along the fence (so you have access to all of the front)?

I think you could do the pole beans on string (I wonder if fishing line is too slick though) but I think perhaps the cukes need a something a little bit heftier. I'm just guessing, so take it as you will...

Here is a link that might be useful: Tales of a Transplanted Gardener

Have two 4x4 raised beds made from 2x8's. And they are abutted against the fence. The first two rows are cukes and beans, so thus the furthest any of them are from the fence are roughly 2.5 feet.

Yesterday I actually set up both a trellis with nylon netting going through the middle of the rows, AND drilled four inch screws every two feet up the fence posts, and then ran twine horizontally between them.

Thanks anyway.

I planted more beans than ever this year. I ran out of room, so I planted my cornfield beans in pots and set them next to the wooden fence. I also put up a nylon trellis. They are just about to start climbing the trellis.