Please let me know if there are any legal loopholes that I can bring up contesting the charges
No.

You signed it.

It's legal.

You breached it.

You pay it.

The $600 is liquidated damages which allows the aggrieved party to collect it without proof of damages. Hence, mitigation is not required.

That doesn't even reflect their actual business costs when the whole cancellation process is online.
No.

Their business costs include not being able to find a replacement for you any time after July 15, a period during which students have already made all their living arrangements and the chances of getting new applicants after that are slim.

The uncertainty under those conditions is what makes the $600 fee valid.

Furthermore I was not allowed to inspect the apartment before signing.
You could have insisted on an inspection and walked away without signing the contract. Taking the apartment without an inspection is on you.