How can I increase deck board gap without removing the boards?
You could install three identical blades in your circular saw with the teeth staggered, then run that down the channel. The saw should follow the gap fairly well, but you'll want to brace the saw with a firm grip to prevent wobble and keep things looking very straight. This should get you about 5/16". Be sure to set the depth properly to avoid damaging your joists, and be aware of the increased tendency for kickback. 

Find a roundover router bit with a small guide that just fits the gap, and run that down as well. If you're lucky you can just run once in each direction (this reduces fibrous texture with softwood). If the bit guide is too narrow you'll need to go both directions while in contact with each board. 

I'd actually borrow or rent a random-orbit (plate style) floor sander and get things level beforehand. If the boards aren't perfectly flat with respect to each other your bullnose will vary quite a bit.