What follows is a suggested approach to tackling impediments on the critical path within a scrum environment.
In another life, I was in the Royal Navy serving at sea in an operational environment, and we used to "play" war games. During a war, the control of the ship shifts from the captain and the bridge to the Ops Officer and the Ops room.
Various teams across the ship are working on understanding the threats to the ship and the opportunity to attack targets. The sonar team will have contacts that they are assessing, radar will be picking up contacts, communications intelligence will have information on aircraft chatter etc.
The Ops team are assessing threats in real-time and the individual teams are all working on providing more information to the Ops Officer on when to launch weapons or countermeasures...
"Launch, launch, launch, bearing 274 degrees"
Upon a communications analyst hearing missile away on aircraft chatter, they scream that a launch has occurred and the bearing. The Ops Officer then turns the ship towards the missile to present a smaller target and the entire ship focusses on the immediate threat...
I'm currently working with a team who ARE the critical path for a major programme of work, we're hitting impediments on a daily basis and have adopted an approach similar to the above.
As soon as an impediment is hit, we pair up. (Alot of people will already be pairing). The pair is then time-boxed at 20mins to identify potential solutions and move to resolution. If no resolution is on the horizon within 20mins, the entire team stops, the problem is white-boarded and discussed to identify a way forward.
The negative side is the 30 mins that could be lost for the entire team during this period which is why I would only suggest this for critical path items. However the benefits are transparency, lots of minds on a single problem, sharing the load and risk, building team cohesion.
Just a thought for your toolbox.