I didn't use an Amiga to "run" a business, but I did use it professionally.
I was working for Digital Eclipse, and game developer around 1999-2005. I was working as an Artist/Animator working on Game Boy Color and then Game Boy Advanced Games. I brought my Amiga 3000 to the office and several of the the other artists and I used it for art production. We used the a Rombo 24RT pro along with a video camera and Take2 pencil test animation software to test our animations which we will hand drew. Then I pulled the grey scale frames into Deluxe Paint V and drew the individual sprite animations over the top. I also used Dpaint extensively when I worked with the team porting Dragon's Lair to Game Boy Color. (not an easy feat). I was given access to the original animation frames from Bluth Studios. I would resize the frames using ADPro and then pull then into Deluxe paint for pallette work and clean up. Something that was super helpful about this process in Dpaint was that I was able to isolate a single color in the pallette and frisket lock that color. I could change a 16 color image to a 8 color image by using a dither pattern between 2 colors.... anyway... just some old tales of using the Amiga even in the new millennia to make professional products!