My lovely Paint gelding (a sabino/overo) has extremely fine hair, and his mane is thin enough that all I've ever been comfortable doing is cutting it. He also has several whorls that affect the way the hair grows, so if it I cut it too short he has cowlicks.
The girl who is part leasing him has her eyes set on Lendon Gray's Dressage4Kids in July. He hasn't needed to be braided for the few shows he's been in. I figure we really need to identify a style, find the directions, and practice. Continuous/French braids (I don't know the difference) pull out. Small button style braids are too small to look good. His forelock is miniscule so I plan to leave that unbraided.
I would braid with very thick yarn (to add bulk) and make the braiding relatively loose and make "hunter" type braids. With these you braid about a 3" section with yarn interwoven and tie off at the ends then pull the yarn ends up through the root side of the mane, turning the braid under. Then use an embroidery needle to pull the yarn ends through the top third of the loop, tighten them and tie them around the relulting bump. Hard to explain in words, but I bet you know what I mean. I would probably even double the yarn.
The button braids can work...just add more than one piece of yarn as you braid down (if you use yarn). As you begin the braid, rather than incorporating just one piece of yarn, use three or four (or whatever!) and just divvy them up amongst the braid sections. Braid down...tie off all yarn. Then, roll up the braid and tie off yarn again around the braid. The extra yarn will beef up the braid so it's a bigger "ball" against his crest.
Leave it longer than normal (by 1"-2") so you have a little more hair to work with. This will also let you use a wider bunch of hair for each braid, making less total braids. I put 8 braids in a normal neck/mane. I'd try for 6 and see how it looks. If you still don't have a decent volume of hair with the longer mane and the wider chunks, you can braid in as much yarn as necessary to make it look right. Just make sure you have the right color.
Although I know it is not a popular braiding style, scalloped braids can work on a thin, but long mane, and are easier on the hair if the hair is prone to breakage.
This. Had a fine-maned Appy/TB. Let it grow out a little longer than regular braiding length. He was a chestnut with roaning (horse in my profile pic) and i braided him with white yarn and did scallops. Often got judge's compliments on it, and it's quick and easy to do, and as above, easier on the hair if it tends to break easily. I find if you do a french brain with really fine manes, you have to make it tighter than on a thicker-maned horse and you DO get more breakage.
I would suggest simply letting it grow out a little longer, so that you have more mane to work with once you braid, and like others have said, add a little extra yarn. Even if it's fine, once you start folding up the braid to make the button, the longer mane (and added yarn) will add bulk to the button.
I don't think smaller buttons look terrible if they're neat and even, anyway. Plus, with the added (longer) mane and yarn, they can't possibly be that small!
My mare has a pretty sparse mane, almost no forelock, and cowlicks, too. She sounds a lot like yours (although I suspect yours has an even thinner mane). Here are her relatively small button braids: Echo's button braids. You can hardly even see the forelock one, but she still looks neat and tidy, I think.