When I do it I'm going to use a long cold ferment. A few days long.
If you want to use it fresh you can peel and blanch it, or leave it in its skin and and put it in a hot dry pan like you do for some Mexican salsas. It will change the flavor though, you won't have that garlic bite.
You can also try slicing it, since that breaks fewer cells.
Well as far as baking failures go, that was probably still a pretty tasty one
But yeah, best way to load butter on to a bread thing is to put the garlic in a bunch of melted butter. It's focaccia, it was gonna be unhealthy anyway
Key is to slice it with a very sharp and thin knife. Think almond sliver thickness. The amount of allicin (and wouldn't it be awesome if your daughter's name was Allison lol) released will be minor, thus not killing off the yeast except right against the garlic.
You can also rinse the slivers and let them dry, which helps as well.
You can even do minced if you rinse and dry, but then you don't get the garlic flavor as much, what with more of the good stuff being released and lost.
But, yeah, most people push slivers into the dough right before baking, at least that I've ever seen. When it's used in the dough, it's usually roasted garlic rather than fresh. Again, that's based on what I've run across.