I don't think it's possible to replace the substrate with the fishes in the tank without stressing them.
It's quite disturbing and depending on the age of the tank, can release toxins trapped in the current substrate.
I have done the process you mentioned exactly once. I removed the original substrate over a couple of weeks removing strips of the original substrate, about 1/10 the bottom area per day or two. Plants in the gravel removed area were repotted and place back into the tank along with hardscape that was affected by the process. Once this process was complete, I kept the tank bare bottomed for a couple of weeks. I then rinsed the Black Florite and put it in a bit at a time, over a week. The work was broken up based on how cloudy the water would get each time. I will say it was very difficult to work around the fish, and working around the fish lengthened the process of change over by quite a length. I did not end up with any of my fish dying but I believe they were not happy and I would not do it again. My original substrate was not too deep but if it was the process would have been more difficult, and I would have more risk of releasing hydrogen sulfide. Speaking from experience I would agree with
@MaloK statements.
On the Black Flourite substrate. I spent a few hundreds putting black flourite (sand in my case but I don't think it matters) in a couple of my tanks based information from the internet and other sources. Now, all of that substrate is in my gardens. I found that it is not black like Black Diamond coal slag but more of a dark grey, not that big of a deal. But, I also found it to be very abrasive, not so good for bottom dwellers but also not so good for the fish that sometimes sort through the substrate to find food. It also tended to compact, and I had some plants that did not seem to do as well (mostly the jungle vals), but others seem to do better, for example I had a nice amazon sword (don't remember the species) but it did quite well in Flourite. Finally, the one issue I had with it is that it is partially magnetic, this is an issue because any of the silt, or larger particles stirred up and pulled into the could end up in the impeller assembly. I was using Aquaclear filters at the time and they started getting noisier, sometimes binding. When I pulled them apart I found flourite attached to the impeller. The only way to avoid flourite dust going into your filters is to ensure that the substrate has settled before starting up the filters, ie substrate change without the fish in the tank.
In my opinion the Flourite substrates are good for tanks that are mostly plant oriented, without bottom dwellers, but if fish are your main interest I would be looking at some other substrate. Others might disagree. I did a post about some alternate substrates but not plant specific,
https://www.fishforums.net/threads/various-sands-and-mineral-substrates-compared.479080/. Would be interested in your observations on whatever substrate or combination of substates you might use.