Best way to change strict state gun laws is to replace the people that run the state, and change the laws. Easier to do at state level than fed level.
Problem you have with winning a high court ruling for a state, is that state will do anything and everything to over regulate the laws regarldless of winning at the fed level. We can see this already at D.C. People in these states need to band together for this cause, or it likely will still be too restrictive anyway.
Voting works better at state levels, but there has to be a big push from the people in the state for this. There was a big push in my state several years back for CCW, without that big push and people getting really involved with the state legislators we would have never got our CCW laws changed.
Voting is still the best method. Especially at local and state levels. I hope things work out for the people in D.C. and Chicago, but the people were the ones that let the laws happen in the first place by their voting habbits. Elections gave them what they have today.