The dude who sold you the bike and went to australia. Were you able to let him know your situation ?
For broken cranks, usually just the actual crank pins need repair. Just replace the crank not the whole engine. Why did everyone suggest replacing the engine ?
Every part inside an engine is repairable. A good car mechanic can work on a motorcycle engine without issue. The engines are very similarly built in cars. They just don't rev as high as a motorcycle though.
I suggest joining a gsxr600 motorcycle forum and ask for advice on what is the symptom.
They can guide you on exactly what needs to be repaired. Or ask for a service manual and do the work yourself. It's super rewarding.