I've developed the opinion that you don't have to get up early for Javelina...for deer you get up early and are set-up sometime an hour before shooting light comes around and expect to see deer moving around right at first light. W/Javelina I don't think that time of the day is any better than any other...or any worse.
So, sleep in, get up at daylight, cook a good breakfast, leave your coat in the whatever (tent or camper) and hit it later than you normally would.
I also don't think they stray far in the dark. I once got my pig at about 9-10 am at about the same place the the daylight ran out on me the day before. I went about 1/4-1/2 from the spot, into the wind and there they were.
You may also try a varmit call. I don't know if it spooks em, but I know of one guy that has had em come in when he was calling yotes.