You have legal rights and some leverage. These may help:
http://www.lsc.state.oh.us/membersonly/employment.pdf
"Every covered employer must keep certain records for each non-exempt worker. The Act requires no particular form for the records, but does require that the records include certain identifying information about the employee and data about the hours worked and the wages earned. The law requires this information to be accurate."
"Many employees work on a fixed schedule from which they seldom vary. The employer may keep a record showing the exact schedule of daily and weekly hours and merely indicate that the worker did follow the schedule. When a worker is on a job for a longer or shorter period of time than the schedule shows, the employer must record the number of hours the worker actually worked, on an exception basis."
"What About Timekeeping?: Employers may use any timekeeping method they choose. For example, they may use a time clock, have a timekeeper keep track of employee's work hours, or tell their workers to write their own times on the records. Any timekeeping plan is acceptable as long as it is complete and accurate."
http://www.dol.gov/elaws/esa/flsa/hoursworked/default.asp
"The amount of pay due an employee cannot be determined without knowing the total number of hours actually worked by that employee in each workweek. An employee must be paid for all of the time considered to be hours worked and all time that is hours worked must be counted when determining overtime hours worked."
http://www.dol.gov/esa/regs/compliance/whd/whdfs21.htm
See: four criteria which must be satisfied....
If they are violating State or Federal Law, you have a case!