I suggest using a software like GeoSetter (google for a link). It will adjust itself for one time zone if you set an offset for it. You may have to play around a bit to get the right adjustment. The best way to figure the adjustment out is to take a photo of the logger's time and compare the time stamps.
GeoSetter will then let you adjust the photo EXIF for the correct time zone, if you want... Although, I'm not sure how well it will do if your photos are in multiple time zones. I've never tried that myself. The few times I crossed zones, I didn't worry much about the time stamps for that day.