Weigh out the surfactants (the SCI, SLSA, coco glucoside, and coco betaine), the shea butter, and the BTMS in a double boiler insert, or in a bowl that can be heated over a pan of boiling water.
Begin to slowly heat and melt the ingredients over a double boiler, stirring until the ingredients have fully melted.
This mixture is very thick and difficult to work with, so it's really impossible to let it cool before mixing in the other ingredients. You'll want to remove the mixture from your heat source and add in the other ingredients, working quickly.
Do your best to fully incorporate the preservative, vitamins, and essential oils. Immediately press the mixture into a bar mold. I use silicone molds meant for bars of soap.
You can help smooth the top of your bar by placing a sheet of parchment or wax paper over the mixture in the mold. Carefully rub over the top of the bar to smooth it.
Optionally test the pH of your shampoo bar by running some water over the finished bar and testing the lather with a pH test strip. Because this is a solid product, it's impossible to otherwise test the pH. We're looking for the pH of the lather obtained using your shampoo bar in your water (with whatever preservative you chose to use, and whatever optional ingredients you may have added). This will help us determine if it would be best to adjust the pH of our next batch. The pH can be lowered by adding a few drops of lactic acid. (It's unlikely that you'd want to raise the pH, but that can be done with some NaOH carefully dissolved in water.)
Once your shampoo bar has cooled, you can remove it from the mold and allow it to dry further. Unlike homemade soap, this shampoo bar can be used immediately. If it's too soft, though, you can let in harden up slightly by leaving it to dry for a few days. (This can occur in regions with high humidity.)