That would be a ton of back pay.
Contact your Business Agent with as much documentation as possible.
Is there evidence that he lied vs was misinformed?
What did the previous drivers experience who you replaced?...8 or 4?
If it was bid as a part time job but should have been full time, it may need to be re-bid. At that point you may not win the bid and your claim for back pay may be toast. Or you may not even be qualified to bid on the full time bid.....Perhaps only full timers can bid. You also may be sent back to your previous job.
Are you a union member or a free-loading scab?