You should be able to apply for a longer extension/deferral of the deadline into the summer if needed. They might need evidence of the reasons you’ll need longer. You have a valid reason (it was your supervisor who gave you the wrong information and guidance, confirmed by your leader )
Check the policies and procedures for requesting this, and also worth asking for support from the student union too.
If you can, get as much of what’s been said in writing in case they ask for evidence. Make sure to include detail on what you’ve been told, what you were told initially and that what’s wrong and what need to change from what the leader said.
Do this ASAP, also email the main department office, letting them know that you are intending to this, in case they can offer support or need to process anything (if not included in the policy)
They shouldn’t deny this, given what you’ve said, it was their fault and given the scale of changes needed so they should be reasonable to this request.
Make sure any deferred or extended deadline submission is not put through as a resit and does not have a cap on your grade too!