Regexen problems? Well the rule is that it will work really really hard to find a match. So figure out why it is finding the unwanted match and deny it.

Well on the second substitution it is clearly able to match "0+" after a 1. Well does that fit the rule? Why yes, the preceeding "1" is not "^", so it can match What to do? Why deny it a digit there. That gives us:

s/(?<![\^\d])(?:\d+\+)//g;
#     ^^^^^^ <- was just \^ before
[download]

which does what you asked.