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Add a black umbrella to each satellite: when they pass through the critical region where they are visible in the night sky while still being sunlit, pop the brollies up. We will fly them in the shade!

You could paint them black but they’d probably get quite hot.

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Won't the shade then reflect the light instead? It's nighttime, so sunlight will be aimed up, from the Earth-based observer's point of view, so the shade will need to be pointed down in order to shade the satellite.
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If you blow up a satellite, half of it will end up going slower and half will go faster. The slower bits will probably burn up nicely, but the faster bits will just elevate their orbit.
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It'll elongate the orbit, which is a bit better of a scenario than elevating it wholesale.
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I doubt they will elevate their orbit by enough to be a problem. Some bits will come down in hours, some will come down in a year - even in the worst case where it takes out everything in low earth orbit in 5 years everything will be clear and we can start over. Higher orbits are the real worry, even the things slowed down mostly stay in orbit for centuries - but higher orbits are mostly a lot higher.
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