As an outsider looking in, I'd recommend baby steps.
The first steps I would recommend would be to make it illegal for a civilian to possess automatic weapons and put a limit on the size of the ammunition clip.
If found with such a weapon, the individual would receive an instant fine and confiscation/destruction of the weapon.
The only thing this would do would make it an anomaly to see someone with a 25 round clip and/or here the rapid fire of an automatic.
Once it becomes uncommon to see/hear these unique weapons, then the weapons will become the sole possession of the criminals. (This makes it easier to enforce - when found)
Knowingly, these steps would not prevent these types of killings, but they may reduce the number of people that are injured/killed, and give a better chance to flee/fight while the individual reloads.
I agree with baby steps. I do not think law enforcement in particular should move on this. I think the research phase should take place now based on the risk level being moderate. I think there is time to design effective policy based in science and do not think hysteria should interfere with the scientific inquiry into this problem.
I do think more funding should go into studying the causes of mass shootings and of violence in particular. Science uncovered the genes associated with violent behavior. Science uncovered that the brains of psychopaths are wired different. We need more science (facts), more data analytics, and less hysteria.
There is no evidence to suggest any gun control policy thus far has had an impact on the outcome of mass shootings. There are stray cases such as the shooting where someone else had a gun and shot dead the shooter but there hasn't been enough to know the impact. Data science would allow for analysis of the outcome in such a way so that we can figure out the underlying factors and perhaps find out a precise policy which can make a difference.