Once the first layer has been removed it's easy to cut inside the edge to make it deeper and repeat the cross hatching and chip removal.
Old needle files can be ground down to make very useful small chisels for removing the chips and cleaning the bottom of the hole and tidying the edge. A small grind wheel which fits in an electric drill only costs a few pounds and is very useful for making/modifying tools.
The great advantage of these tiny chisels is they are very easy to sharpen, a quick wipe on an oil stone or wet & dry paper with a spot of oil and you can have a razor sharp custom made tool just the right size for your job.
The knife I use is an old fashioned craft knife (Stanley knife) but the two halves have been opened up and filed flat so they close tight and grip the blade to stop it rattling about. A scalpel would work just a well, but the Stanley knife gives plenty to grab hold of and room for two hands. I'll hold it steady with one hand and then use the thumb of the other hand to apply a controlled leverage for a powerful cut which won't shoot off cutting across the surface of the bow.
The final pic shows the inlay having been filed to be a good fit into and nosed into the hole with it's back edge sticking up. The knife can then score an accurate line for the back of the hole ensuring a snug fit.
I like this shield shape for an arrow plate. Often they are made with simple straight lines, like a rectangle with a triangle on top like the end view of a house.
To me that looks cheap and is often sloppily done.