I'll go along with most of that except

If you use an empty pattern in the substitution, Perl will do the right thing. Another five characters.

Without the negative lookahead, the regex will produce a very high proportion of invalid expressions because it will insert an operator at the very end of the string:

9+8*7*6*54/3-2/1-
-9-8-7*6+5/43/2+1
987+6/54321
98/7-6+5-4/321+
9*8/7/6/54-3/2-1
9/876*543/21
-9*8/76543*2-1-
-987/65-432+1*
9*8+7+65*432*1-
9876/5*43+21
9876-54321*
987/6-5-4/3-21/
9-8+7*65432+1
98765+432*1+
-9*8-7*65432-1+
9+87*6543*21
9-87*65*4-3-2*1
-987654-321+
98*76/54*32*1-
-9-876/5-432*1*
-987*654+321
9/87+6543*21
98-7654/3+21
-98*7-6-5*4321
98+7+6/5+4*3+2-1
-98+76+54*3/2+1/
9876543/21
-9-8+76-54321*
[download]

Not always, and so it can be expected to still produce occasional correct answers, but it will take much longer and somehow offends my sensibilities :)