How to put the bacon IN the burger?
I think the options you describe are very manageable. We have two kinds of bacon burgers where I live (apart from the regular piece of bacon loosely on top of a patty):


the bacon is cooked, then crumbled/chopped finely and mixed in with the raw mince meat. You can choose how large you want your bacon chunks to be.
the bacon is raw, and wrapped around a patty. If you wrap it well (with lots of overlap), the bacon stays in place. Be careful, as bacon can shrink a whole lot.
If you want to be extra safe, you can use a toothpick to hold everything in place.