I don't think OP has said that his/her firm has forced him/her to shorten the notice period. Tendering does not equate to shortening notice period. As a matter of practicality, I doubt it makes sense to ask for compensation in lieu of notice, particularly since it may likely lead to a gap in OP's CV –*assuming that OP will face difficulty finding another job. Might as well just tender, serve notice, and concurrently find a job.