Slider: Odd value when sliding past min/max value, only when 'step' represents < 1px

JSFiddle example: http://jsfiddle.net/C4W3z/

The example link above explains the problem succinctly. Below is just my use case to explain why increasing the step value to represent >= 1px is not an ideal work-around.

My app's slider represents a time range over several months. I want the step to be minutes. Understandably, dragging the handle one pixel changes the value multiple minutes (since there aren't enough pixels to represent every step), but using the keyboard arrows moves per my 1-minute steps. This works as desired: quick moves via mouse, and fine control via keyboard.

On Firefix, the odd behavior is when the handle is at the max. Then, if you click and drag the handle to the right by exactly one pixel, the slider's value goes to less than max. Sliding further to the right pegs at max, as expected. On Safari, the error is on the min side. Looks like a float rounding error?

It's obviously a minor issue, but my users often scroll to/from the max value, and my app appears jittery there. (My workaround will be a separate control for fine adjustments, so I can keep the step value >= 1px.)