Booleans will be tough with this - I’d recommend trimming using outlines instead, then build the inside surfaces.
For recesses that end in sharp points:
Draw the three curves that define the shape (each side and the curve at the bottom.)
Trim the surface of your part with the side curves.
Move the bottom curve to the height of the lowest part of the recess.
Move the end points of that curve up to the end points of the other two curves (maybe use SoftEditCrv if simply moving the end point is not the right look.)
Use Sweep2 to build the surfaces.
If the part ends with a squared-off shape, then just stop your 3rd line (the low line) early, just like you see in your example image. Draw the lines that connect the squared end to the end of that line, and build surface in there. It’s really not super hard to just build everything in this manual way.
I would draw a single curve in the center of the design elements where you want the sharp edge to be, lower the curve by the desired depth, then do a loft from the edges of the top surface to the curve to create your carving effect. This example uses 2 curves on the surface that I use to trim the desired shape, then a curve draw from point to point, and lower the control points in the middle.