Never had a problem finding a bed early last August on the first half of the Frances. You might want to book a bunk at Roncesvalles if you think you'll make a late arrival. I always tried to walk so that if the albergues in a small town were full, there was always another town less than an hour's walk further down the trail. Never had to do the extra hour.
2pm is a good time to aim for as due to Spain being in the wrong time zone, it is when midday is. As for starting at 6am...it will still be quite dark so you might want to take terrain into account when deciding when to start.
What do yo do when you get there at 2pm? Find your bunk, wash yourself, wash your clothes, dry your clothes, have a siesta, pack your bag ready for the next day, tend to your feet, have a drink or three, eat, take a stroll around the town if there is one, that sort of thing. Take in your surroundings and enjoy. My top tip: never, ever, ever stay in a big room albergue.
Has anyone noticed how "albergue" gets underlined as a misspelling when composing a message? Alanis Morissette never mentioned that in her song.