There's a little cave to the left you could of went to. It over looks the vault entrance, gives enough running space for a long jump to charge to foh. Hell the gap is smaller than I really thought and I find myself overcompensating a lot.

I have no shame in stating that's the only way I ever clear that section. Did legit first time ever in vault but then got lazy. Just remember to have stiker equipped. But embarasing otherwise.