Title 29 C.F.R. 541.304 provides salary-exempt status to physicians. So, your employer does not have to pay you overtime.
Additionally, Title 29 C.F.R. 778.114 provides, "(a) An employee employed on a salary basis may have hours of work which fluctuate from week to week and the salary may be paid him pursuant to an understanding with his employer that he will receive such fixed amount as straight time pay for whatever hours he is called upon to work in a workweek, whether few or many. Where there is a clear mutual understanding of the parties that the fixed salary is compensation (apart from overtime premiums) for the hours worked each workweek, whatever their number, rather than for working 40 hours or some other fixed weekly work period, such a salary arrangement is permitted by the Act if the amount of the salary is sufficient to provide compensation to the employee at a rate not less than the applicable minimum wage
rate for every hour worked in those workweeks in which the number of hours he works is greatest, and if he receives extra compensation, in addition to such salary, for all overtime hours worked at a rate not less than one-half his regular rate of pay."
At this point in the analysis, if you and your employer have an understanding that you will be paid the same salary regardless of your hours worked, and your pay when divided by the number of hours worked, is not less than minimum wage for your jurisdiction (Indiana: $7.25 per hour) then the agreement would be enforceable.
The problem is that you do not apparently have an understanding of the agreement, because there is this issue of when your workweek begins.
Title 29 C.F.R. 778.105 provides: "An employee's workweek is a fixed and regularly recurring period of 168 hours—seven consecutive 24-hour periods. It need not coincide with the calendar week but may begin on any day and at any hour of the day. For purposes of computing pay due under the Fair Labor Standards Act
, a single workweek may be established for a plant or other establishment as a whole or different workweeks may be established for different employees or groups of employees. Once the beginning time of an employee's workweek is established, it remains fixed regardless of the schedule of hours worked by him. The beginning of the workweek may be changed if the change is intended to be permanent and is not designed to evade the overtime requirements of the Act. The proper method of computing overtime pay in a period in which a change in the time of commencement of the workweek is made, is discussed in §§ 778.301 and 778.302."
Here, it is possible for the employer to set your personal workweek commencing and ending at a certain hour. The issue finally devolves into a question of whether or not the employee handbook creates an implied unilateral contract upon which you are entitled to rely.
In Orr v. Westminster Village North, Inc., 689 N.E.2d 712 (Ind. 12/15/1997), the Indiana Supreme Court held: "[A]n employee handbook may constitute a unilateral contract and bind the employer if the following three criteria are met: (1) the language of the employee handbook must contain 'a promise clear enough that an employee would reasonably believe that an offer had been made;' (2) the employee handbook must be disseminated to the employee in such a manner that the employee is aware of its contents and reasonably believes it to be an offer; and (3) the employee must accept the offer by commencing or continuing work after learning of the terms of the employee handbook."
The above-quoted criteria is the key to winning your argument. From what you have described, it seems pretty clear that the handbook states that each employee's workday hours commences at midnight. Absent some other unknown, this would appear to satisfy at least one element of the test, confirmed in Orr.
Unfortunately, in order to prevail on this issue, you would have to sue the employer -- and that means you could be fired in response. In other words, you could win your 32 days pay, and lose your job. So, if that's something which would be untenable to you, then you may have to give up on the additional days of unpaid time.
You could obtain whistleblower protection by filing your claim with the U.S. Department of Labor. However, experience suggests that the DOL isn't much interested in claims by highly-compensated professionals. DOL is more interested in a large number of minimum wage workers being exploited by a national employer. So, while you could file such a complaint, it may end up going nowhere, and you would be back to a decision of whether or not to sue your employer, and thereby risk the loss of your job in retaliation.
Hope this helps.