So I went and bought another blind. Fortunately this was a small one and only £7. Then I took the one that fell and cut it in half. Glued these pieces on to the bottom of the two appropriate blinds. Worked out okay. They've been up for...four hours. No problem so far. And now they cover the whole window.
They don't look great but even without the glued on bit they didn't look great. And the second this lease is over I'm out of here. If not sooner.
Tomorrow I have to cut the big blind in half and fix the last two blinds. It's not hard. Just hot glue.