That’s to be expected. You have repaired the clipping, and the clipped part is now louder by 4.1 dB.
So it sounds OK now?
You might be interested in Steve’s Limiter effect: https://forum.audacityteam.org/t/limiter/21818/1
Scroll down to the seventh post in that thread to get the latest version. Once you’ve downloaded it, put it in the plug-ins folder inside the Audacity folder (or wherever you have installed Audacity) and restart Audacity. Read the thread for instructions on using it. You might be able to get that 4.1 dB back.
Thanks for all the suggestions. I will investigate them as I learn more about audacity!
I realized that I could just zoom in and pick out the specific parts with clips, and fix those - select, deamplify, fix, reamplify. There’s only one little fraction of a second where it clips badly. The original volume is preserved, and because the clips are so short, you don’t notice the volume change on those parts.
Try the limiter effect as suggested by Bill. Basically what that does is to reduce the level of loud peaks that are above the “threshold” and (optionally) amplifies the entire waveform up to use the extra available space. It’s similar to what you are suggesting, but automatic, so it won’t take a week to process the track.