WARNING: Based on Sleske comment, I jumped to a conclusion that I most likely shouldn't have in my original answer, so I've modified my answer to take into account the new information he provided.
From your own employee handbook, it says:
that salary employee pay will not be reduced for "partial day absences for personal reasons, sickness, or disability."
In other words, your employee handbook says "employee pay", not PTO. That distinction is important because that distinction was made in a California court case where the employer won on the same issue.
The court reasoned that requiring an exempt employee to use accrued PTO leave does not result in any deduction made from the employee’s salary...
In General Atomics, the appellate court found that deductions for any duration are legal. [...]
The General Atomics case opens the door for partial-day deductions of any length. But just because you can, should you? Robert A. Jones, a shareholder in the San Francisco office of Ogletree Deakins, observes: “Many employers believe that requiring partial-day deductions from PTO is generally inconsistent with the level of responsibility and authority of their exempt employees and may have a negative effect on employee relations and moral.”
Granted, California is not New Hampshire, and personally, I feel that court decision in California was goddamn awful, but if that distinction holds true in California, that same distinction could hold true in New Hampshire as well.
That being said, you should still contact the New Hampshire Department of Labor to ask for their opinion. Dealing with wage theft/vacation theft is their job. And hopefully, one can hope that New Hampshire is doing things differently than in California.