It's important to distinguish the difference between a stain and a dye. You probably already know this, but a stain is basically pigments suspended in a thin binder, or glue. They only color wood on the surface, by the pigment lodging in the pores of the wood. They usually don't do much to a closed grain wood like poplar. Dyes, however, are a liquid solution of totally transparent dyestuff. It's kind of like KoolAid. The liquid goes deep into the wood, and colors the wood from within. Because dyes are transparent, they give much more vibrant colors than stains.
A good quality black aniline dye should get that poplar dark as night. It shouldn't affect your epoxy filling much, if you have sanded it smooth, and left no sand scratches for the dye to go. I would recommend sanding the epoxy to 600 grit or so, and wipe a little of the dye on, to see if it marks. The dyes are all very similar, the main difference to us being what they are dissolved in. They are dissolved in oil, water, alcohol, acetone, and a variety of other chemicals. You might want to try a water soluble aniline dye, as the water would be too weak to "bite" into the epoxy, and cause discoloration.
I hope this helps. If you have any other questions, please feel free to ask.
Sam