Can I use knee bracing to cantilever a deck further than code allows?
That seems reasonable, but your local inspection office is the ultimate authority. You should sketch it up and meet with an inspector.

I'd be a bit concerned about drilling completely through the pilings, though (which I assume are concrete). That's a lot of rough treatment for a relatively thin structure. Instead, I'd use expanding anchors and lag screws.

You'd also have to connect the top of the knee brace to either the pilings or the existing joists to keep it from rotating outward.