Seems to work here. Update: which is obvious since I'm using single quotes (non-interpolative) and you're using double-quotes (interpolative) so the $1 is being interpolated and the replace part of s/// actually looks like brianbob. Try something like this (i.e using single-quotes) and your code should work fine

perl -le '$_="brad123bill"; print; s/brad(.+?)bill/brian$1bob/; print'
brad123bill
brian123bob
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HTH

_________
broquaint