This may be a rotten suggestion due to my unfamiliarity with such matters. But, would a temporary fix be possible by bisecting lengthwise a new section of identical corrugated pipe (of the same diameter) and securing/sealing it in position over the rusted bottom of the old pipe (using rivets, sheet-metal screws, adhesive, etc)?
The half-round pipe-section could be inwardly compressed (using temporary draw-wires) to permit its insertion within the old pipe. Of course, adequate access to secure & seal the upstream edge of the half-round might pose a challenge - but I think it is do-able with a little thought. Wonder if there is some type of adhesive that would hold the bisected length of pipe in place (possibly using two or three scissor-jacks to apply internal pressure while it cures).
Go easy on me! It was just a thought! wink

EXISTING

PROPOSED