MacOS – Damaged hard drive due to magnet damage (Macbook Pro)

You should be able to use dd to destroy the partition's header. You can then format (erase) it and run the install.

From the installer run Terminal and type the following:

dd if=/dev/zero of=/dev/disk0s2 bs=1024 count=1024

Do be warned, this will irrecoverably destroy all data on that partition. But it looks like that's what you're expecting. Make sure you don't accidentally target the wrong thing.

Also note that I haven't done this, exactly. I've used this technique to destroy the entire partition table, not just a single partition. But I think it should work.

When you're done quit Terminal and run Disk Utility. You won't get any complaints about Core Storage.

The fact that it boots perfectly fine in safe mode points to a problem with your graphics card. Safe mode disables all hardware drivers besides those absolutely essential to the operation of your system, and that includes hardware graphics rendering. The reason your graphics are so choppy in safe mode is because everything is rendered in software (i.e. by your CPU) rather than in hardware (by your GPU). I doubt it's a hard drive issue simply because you have no problem installing ML or booting up.

The good news? Since your repair was around a year ago, you might be able to convince the Apple Store people (talk to the manager) to replace your logic board for free.