Alot of the apparent crunchyness actually seems to come from bad editing in the book, making some rules unclear, unwritten or hard to find.
Once the dice pool have been properly establish, the only thing left to calculate in a situation is edge. I suspect that we may have to establish a system for all the off turn actions in combat though, like a way to apply the dodges and hit the street before or after so it doesnt not take a full post.
I also think that edge will bring some interesting strategies for those who take care to exploit it, like an actual use for splitting your dice between 2 targets to farm some edge in a fight. Going for anticipation for Full dice on multiple targets, add edge to your pool dice for the tough one or regaining health in attrition fight can all change the balance of a scene beautifully.
Up to now, the greatest slowdown i've seen is getting familiar with the setting and its perks, both social and technical.