> your paycheck--the dollar amount you brought home--would be cut in half. However, your car payment, your mortgage, and your credit card bills would stay at the same nominal value.

Not necessarily. If the transition to a deflationary economy is slow and planned, then expected deflation would start to be considered in the interest rates of your car payment, mortgage, etc. i.e. interest rates would become negative not long after inflation becomes negative.

If employers are capable of negotiating deflation adjusted salaries, then market pressure is capable of forcing companies to adjust their prices and interest rates to deflation.