Have written on this topic many times. Last of the night is the best. Why? They are more likely to be horny, they are more likely to be receptive to a dude that gives her attention or chatting and seems more like a pal than a filthy customer manhandling her, and of course there's the after hours part. Fewer interruptions, and loads of chances for overtime and extras. Even if it doesn't turn out awesome, you can earn so many bonus YMMV points to use next time. Plus, if you're into AMP sleepovers, there's your time. Earn those YMMV points then cash them in! I get best effort from AMP girls at last hour, even ones I never saw before, but especially ones I've seen several times.
I understand the point that they are "fresh" first thing, but most places have a shower, and I hear they have SO MUCH soap, alcohol, wipes, and blue toast. Offer to give them a TS after their long hard day.