We're much closer than you think
Jelly, Score 1 * 8 bytes = 8
String zip:
+Ẇɼ+

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Cantor pairing function:
+ẆL+

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We use the fact that the Cantor pairing is equal to
$$ {n + m + 1 \choose 2} + m $$
Where the left term just happens to be the number of nonempty contiguous slices of \$m+n\$. This saves two bytes per program over the naive +‘×+H+, and one byte over the (less naive) +‘c2+.
Conveniently, in Jelly + zips strings (I had no idea!).
Explanations:
          Implicit input: strings s1, s2
+         Zip s1, s2.
 Ẇ        All nonempty slices.
  ɼ       Save the result to register (ignore previous 2).
   +      Zip s1, s2.

          Implicit input: numbers n, m
+         Compute m+n.
 Ẇ        All nonempty slices of implicit range m+n.
  L       Length.
   +      Add m.    


Note that there are many ways to get 4 for the pairing function (+R;S, +R+ƒ, etc)