I tried bending the trunk more, but it only gets back in its place. Would the action of bending it daily or a few times a week help train its shape?
No, not at all. Bending is done in one go. Bending several times can adventure the health of the tree.
Your issue is bad wiering and maybe too thin wire. The wire you have put on is doing nothing. Redo the wiering correctly and with a thicker wire and you will see it stays as you want. And as a bonus you will not need that ugly plastic rope you have put on it.