It turns out that you can use half the amount of BigDye that is recommended by NAPS/SBC for Sanger sequencing and have no noticeable drop in sequence quality. The updated recipe for the working dilutions:

BigDye 3.1 stock      0.5 parts

BigDye buffer            1.5 parts

Water                       1 part

I will prepare all future working dilutions using this recipe and put them in the usual box in the common -20ºC freezer. For more details on how to prepare a sequencing reaction see this post, and for how to purify them see this or this posts.