Hi Swainey... welcome to GoY.

Try GENTLY bending the top parts of the tall stems, so that they are more horizontal than upright. You might need to do this gradually so that they don't snap ...

... tie them slightly over, and then go back some days later and encourage the stems over, to less of an upright position .. this should encourage more bud growth ..

I hope this helps.

Interesting question which I've added to GoYpedia.

You'll probably get more ideas in other comments.

I find that as tt says the soft growth needs to be tied in as close to horizontal to get plenty of buds. failure of buds to open is often linked to buds getting wet and then fusing the petals together.

Roses do have to be helped to cover an arch and not just grow up the side. Over the years I have found that with climbing/rambling roses bending the stems as they grow slows the sap and encourages buds to form. When I planted 2 roses on my arch I put them away from each base of the arch and bent them towards it and when they reached the arch I continued to tie them in at an angle so they did not go straight up when they reached the top I bent them over to cover the top of the arch and they have knitted together.
On your arch you could gently push the growing stems back and forth through the spaces and that will bend them enough as they grow. Also bend them over the top of the arch and not let them just go on up. Bend very gently as you dont want to damage the young stems.