Thank you. I believe I've resolved the issue. Although I haven't tested it on my main project yet, I'm confident it will work.

By using trim instead of projection, I managed to create an indented design.
I realized my mistake was performing a boolean operation on the "Joined srf" which was obtained by the trim operation. By keeping a copy of the solid and performing the boolean operation on that, I was able to get a solid.

Since I was able to get a 'Solid', I shouldn't have any issues with the orientation of the faces anymore. I will confirm this in my upcoming checks.