I've got a saw that swivels side to side, and also tilts
I guess if you have what I understand to be a "compound mitre saw" then I don't understand why you are cutting with "the material laying flat and the blade tilted". You can't possibly hit your mark like that without a little speculation as to whether or not the blade in in the correct relationship to the material.
Why wouldn't you stand the material "up" against the fence and swivel the blade to a 45 degree angle like any carpenter would do? How wide/tall is this "regular base trim"?
Also, I would cut my 45 for the outside corner then get the necessary measurement to fit the inside corner at the opposite end of the piece and "cope" that end about 1/16" longer than necessary so-as to be able to "snap" the material into place. This insures a proper fit at the outside corner and a snug fit at the opposite inside corner.
Rather than using a pencil mark I would be using a utility knife to make precise marks on/in the material.
Maybe I'm missing something here!