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.

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.

Don't be so sure: https://stuffin-space.vader.zone/

The Iridium-Kosmos collision fragments have been up there since 2009, and that's a massive spray of junk just from one disintegration in LEO.

In either case, you will increase the section area / volume ratio, what makes the fragments fall from LEO faster.

It'll elongate the orbit, which is a bit better of a scenario than elevating it wholesale.