Can we say "a" dice?
Well, I confess that I say "one dice."
I'm not a teacher, but I write for a living. Please don't ask me about 2nd conditionals, but I'm a safe bet for what reads well in (American) English.
I too am a "one dice, two dice" person, along with everyone I've ever played Monopoly or Snakes & Ladders with.
I die/dice but don't feel strongly either way.