Will ice cream freeze faster with frozen brine or adding salt to ice?
If the brine melts at the same temperature you reach with the ice and salt, then it should take the same time to freeze the ice cream since the freezing time depends on heat transfer. The benefit of frozen brine is that there is more heat capacity in the frozen brine than in ice-salt cooled water, so the ice-salt water may become warmer than the frozen brine. 

It may be that there is poor heat transfer from the cream to the ice so it takes longer than you think. Also, if you are the one turning the crank, time seems to stretch out since your muscles get tired and yet the ice cream is still not frozen.