It won’t grow downwards ... I would nip out the growing tip to encourage th weed development of lots of sideshoots you’ll be able to train around the obelisk.
“I am not lost, for I know where I am. But however, where I am may be lost.” Winnie the Pooh
Honeysuckles grow in metres, not feet so I would advise you to try and give it somewhere else to spread its shoots - pergola, trellis panels, tensioned wires between posts........
"We don't stop playing because we grow old; we grow old because we stop playing." - George Bernard Shaw
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It won’t grow downwards ... I would nip out the growing tip to encourage th weed development of lots of sideshoots you’ll be able to train around the obelisk.