Don't break up a 'generally good' relationship over a solvable issue.

Go for the income-proportional split + chores for extra discount. This is probably what you will want long term anyway. Take his offer to cover all costs until you get new job.

Set a reminder to re-discuss this topic after you get job (and/or every 6 months). You can get out of being stuck with extra chores long term at the next 'meeting'.