As has previously been noted, the case volume you want to use in QL is that measured from fired brass. Although fired brass has contracted ever so slightly from its peak volume during firing, which aids in allowing the cases to be readily extracted, it still has the volume that is closest to the maximum internal case volume when the case has fully expanded to fit the inside of the chamber; i.e. the "pressure cell" volume.
Below is a chart often seen on internet shooting forums that lists some average case volume values for various brands/types of .223 Rem brass, which is the parental case for the 300 HAM'R. As you can see, the listed values are from 28.0 gr to 30.6 gr, or a total range of 2.6 gr. Further, none of them actually match the factory preset value of 28.8 gr used for the .223 Rem case in QL. To be honest, I have no idea how they came up with that specific value, although I'm sure there was a reason they did so.
Although very important, case volume is not the sole factor that determines pressure and velocity with a given powder. Other factors such as case shape, bullet weight, start pressure, and primer selection also factor in to the equation. Initially, I would suggest inputting your actual measured average case [water] volume with all the other pertinent cartridge measurements and temperature, then adjust the burn rate (Ba) until the velocity predicted by QuickLoad exactly matches your measured average velocity. I typically refer to this process as "calibrating" QL to a given setup. Usually, once I have calibrated QL to give the same predicted velocity as the measured average velocity for a given charge weight, the predictions will be fairly accurate within a given charge weight range from that point on. One caveat is that of your have to change the factory preset Ba for a given powder by more than a certain percentage, QL has some suggestions for other things to do besides solely adjusting the Ba. I haven't had to do that in a long time and I don't remember exactly what their alternatives are, but they are listed in the User Guide, so you should be able to find them and read up on it.