I understand where you're coming from. I generally try to see WG's at the beginning of the day if I can, usually scheduling for my day off. Two reasons; 1) the same you mentioned, and 2) I just like to be first! I know they see other men, but I just like to be first, haha.
I have seen WG a couple times very late in the day (like 10/10:30pm) and both times she wasn't great. That being said, she wasn't the best earlier in the day either, so that's more the girl than the time I think.
I've never been to HoD, but from what I gather on here, the girls there are pro's, and generally regarded as a cut above the rest, so I think you'll be fine.
Be nice to hear from someone that's visited both early and late though