3^5=243. so use a byte to represent a vector of 5 ternary values, leaving some possible signaling values.

Rather than (indistinguishable?) 0 and -0, why not add back some magnitude in the positive direction?

  { -1, 0, 1, 2 }

is most obvious, but it's not clear whether it's better or worse than

  { -1, 0, 1/2, 1 }

Maybe theoretically (if not architecturally) it would best to "split the difference" between the two and choose

  { -1, 0, 1/phi, phi }

or perhaps the more implementable

  { -1, 0, 1, 3 }

EDIT: Of course you can also go the other way, with

  { -1, 1 }