yes, a lot of companies are practicing this kind of system right now. Especially those with high turnover of employees. There is nothing wrong on their part and you are bound to this contract whether you like it or not.

The only way is to ask your manager to let you go early. That is possible because decision is on your dept manager. Whether he/she want to do it or not is another matter.

My previous company also have similar system. One of my collegue wanted to resign but need to wait 3 FULL months as cannot offset with leaves. In the end, he negotiated with manager. Manager talk to management and they said the decision is up to the manager. If the manager think the dept won't be affected by letting go early then fine. The manager also said, no point insisting the staff to stay when they already want to leave.

In the end, the manager hired a temporary staff to take over the jobs.

Talk to the manager nicely. Tell her you already got another job offer. Ask them to let you go early with necessary deductions. Promise that you will finish up all your pending jobs and handover nicely. Which is another word...won't do it if not let go early....