I have not watched any of the vids and they might have already said what I am about to but...I have done my fair share of inlaying both wood and metal into pistol grips and rifle stocks so I can relay a few pointers that help me do a clean job.
#1 file a slight taper, very slight, on the piece to be inlaid.
#2 use a very sharp Exacto blade to cut an outline of the area to be removed. Tracing around the piece to be inlaid. If need be, lightly adhere that piece to the stock if you are unable to hold it steady as you trace around it with the Exacto but still putting downward pressure so the inlay doesn't slide around while tracing.
#3 Cut toward the outline with your chisel once you have a nice outline, use your non-chisel holding hand in front of your chisel hand to control the chisel so you won't push too far. I use a narrow straight chisel, beveled side down, and from the inside of the design, about 1/16" inch away from your outline, cut out a chip of wood the width of your chisel. At this stage I am holding the chisel almost straight up, maybe 5 to 10 degree angle. Of course once you have this area cut around the inlay perimeter you will lower the remaining wood inside the perimeter and begin the fitting process in earnest.
#4 Use a transfer agent when putting the inlay into the stock to see where you have to remove wood. For metal I use a commercially available inletting black (you can make your own using grease and powdered marking chalk}. I have used red in the past but they also have blue chalk. For a wood inlay I just use a piece of blackboard chalk. You can get all kinds of colors in "sidewalk chalk" for children. Choose a color that will show up well on the stock.
#5, Keep your chisels extremely sharp. I never use (well OK rarely) scrapers but just chisels.
Hope this helps, I'm sure other have their own ways but this method has worked well for me.