You might consider splitting the track between the part(s) that need correction, and everything else. That way, you can just have the pitch correction plugin on the parts you want fixed.
I use Reaper, which is relatively inexpensive and had a pitch-correcting plugin called ReaTune. You can see it in action
here. In the
Manual Correction you can specify exactly what you want corrected - very much like what you're describing. One nice thing about Reaper is that other than a short nag screen, none of the features are disabled in demo mode.
I believe Melodyne has a time-limited demo.